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"\ifx \undefined \poly \def \poly {{\rm poly}} \fi" #
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@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|http://www.math.utah.edu/~beebe/|"}
@String{pub-ACM = "ACM Press"}
@String{pub-ACM:adr = "New York, NY, USA"}
@InProceedings{Akavia:2006:BOW,
author = "Adi Akavia and Oded Goldreich and Shafi Goldwasser and
Dana Moshkovitz",
title = "On basing one-way functions on {NP}-hardness",
crossref = "ACM:2006:SPT",
pages = "701--710",
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bibdate = "Thu May 25 06:19:54 MDT 2006",
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http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
note = "See erratum \cite{Akavia:2010:EBO}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kannan:2010:SMM,
author = "Ravindran Kannan",
title = "Spectral methods for matrices and tensors",
crossref = "ACM:2010:SPA",
pages = "1--12",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
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acknowledgement = ack-nhfb,
}
@InProceedings{Talagrand:2010:MSS,
author = "Michel Talagrand",
title = "Are many small sets explicitly small?",
crossref = "ACM:2010:SPA",
pages = "13--36",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
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acknowledgement = ack-nhfb,
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@InProceedings{Montanari:2010:MPA,
author = "Andrea Montanari",
title = "Message passing algorithms: a success looking for
theoreticians",
crossref = "ACM:2010:SPA",
pages = "37--38",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
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acknowledgement = ack-nhfb,
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@InProceedings{Goel:2010:PML,
author = "Ashish Goel and Michael Kapralov and Sanjeev Khanna",
title = "Perfect matchings in $o(n \log n)$ time in regular
bipartite graphs",
crossref = "ACM:2010:SPA",
pages = "39--46",
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acknowledgement = ack-nhfb,
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@InProceedings{Leighton:2010:ELV,
author = "F. Thomson Leighton and Ankur Moitra",
title = "Extensions and limits to vertex sparsification",
crossref = "ACM:2010:SPA",
pages = "47--56",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kolla:2010:SSN,
author = "Alexandra Kolla and Yury Makarychev and Amin Saberi
and Shang-Hua Teng",
title = "Subgraph sparsification and nearly optimal
ultrasparsifiers",
crossref = "ACM:2010:SPA",
pages = "57--66",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Barak:2010:HCI,
author = "Boaz Barak and Mark Braverman and Xi Chen and Anup
Rao",
title = "How to compress interactive communication",
crossref = "ACM:2010:SPA",
pages = "67--76",
year = "2010",
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http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
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@InProceedings{Klauck:2010:SDP,
author = "Hartmut Klauck",
title = "A strong direct product theorem for disjointness",
crossref = "ACM:2010:SPA",
pages = "77--86",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
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@InProceedings{Beame:2010:HAP,
author = "Paul Beame and Trinh Huynh and Toniann Pitassi",
title = "Hardness amplification in proof complexity",
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pages = "87--96",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
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@InProceedings{Gao:2010:LBO,
author = "Pu Gao and Nicholas C. Wormald",
title = "Load balancing and orientability thresholds for random
hypergraphs",
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pages = "97--104",
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@InProceedings{Bayati:2010:CAI,
author = "Mohsen Bayati and David Gamarnik and Prasad Tetali",
title = "Combinatorial approach to the interpolation method and
scaling limits in sparse random graphs",
crossref = "ACM:2010:SPA",
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@InProceedings{Hirai:2010:MMP,
author = "Hiroshi Hirai",
title = "The maximum multiflow problems with bounded
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http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Madry:2010:FAS,
author = "Aleksander Madry",
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multicommodity flow problems via dynamic graph
algorithms",
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pages = "121--130",
year = "2010",
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bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Aaronson:2010:FCQ,
author = "Scott Aaronson and Andrew Drucker",
title = "A full characterization of quantum advice",
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pages = "131--140",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
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@InProceedings{Aaronson:2010:BPH,
author = "Scott Aaronson",
title = "{BQP} and the polynomial hierarchy",
crossref = "ACM:2010:SPA",
pages = "141--150",
year = "2010",
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http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Ambainis:2010:QLL,
author = "Andris Ambainis and Julia Kempe and Or Sattath",
title = "A quantum {Lov{\'a}sz} local lemma",
crossref = "ACM:2010:SPA",
pages = "151--160",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
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@InProceedings{De:2010:NOE,
author = "Anindya De and Thomas Vidick",
title = "Near-optimal extractors against quantum storage",
crossref = "ACM:2010:SPA",
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year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
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@InProceedings{Applebaum:2010:PKC,
author = "Benny Applebaum and Boaz Barak and Avi Wigderson",
title = "Public-key cryptography from different assumptions",
crossref = "ACM:2010:SPA",
pages = "171--180",
year = "2010",
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acknowledgement = ack-nhfb,
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@InProceedings{Ajtai:2010:ORC,
author = "Mikl{\'o}s Ajtai",
title = "Oblivious {RAM}s without cryptographic assumptions",
crossref = "ACM:2010:SPA",
pages = "181--190",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
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@InProceedings{Goyal:2010:RCC,
author = "Vipul Goyal and Abhishek Jain",
title = "On the round complexity of covert computation",
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pages = "191--200",
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http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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}
@InProceedings{Bhaskara:2010:DHL,
author = "Aditya Bhaskara and Moses Charikar and Eden Chlamtac
and Uriel Feige and Aravindan Vijayaraghavan",
title = "Detecting high log-densities: an {$O(n^{1/4})$}
approximation for densest $k$-subgraph",
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pages = "201--210",
year = "2010",
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bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Bateni:2010:ASS,
author = "MohammadHossein Bateni and MohammadTaghi Hajiaghayi
and D{\'a}niel Marx",
title = "Approximation schemes for {Steiner} forest on planar
graphs and graphs of bounded treewidth",
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pages = "211--220",
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@InProceedings{Dey:2010:OHC,
author = "Tamal K. Dey and Anil N. Hirani and Bala
Krishnamoorthy",
title = "Optimal homologous cycles, total unimodularity, and
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http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Williams:2010:IES,
author = "Ryan Williams",
title = "Improving exhaustive search implies superpolynomial
lower bounds",
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title = "On the complexity of circuit satisfiability",
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author = "Holger Dell and Dieter van Melkebeek",
title = "Satisfiability allows no nontrivial sparsification
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year = "2010",
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@InProceedings{Magniez:2010:RWP,
author = "Fr{\'e}d{\'e}ric Magniez and Claire Mathieu and Ashwin
Nayak",
title = "Recognizing well-parenthesized expressions in the
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pages = "261--270",
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@InProceedings{Braverman:2010:MID,
author = "Vladimir Braverman and Rafail Ostrovsky",
title = "Measuring independence of datasets",
crossref = "ACM:2010:SPA",
pages = "271--280",
year = "2010",
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@InProceedings{Braverman:2010:ZOF,
author = "Vladimir Braverman and Rafail Ostrovsky",
title = "Zero-one frequency laws",
crossref = "ACM:2010:SPA",
pages = "281--290",
year = "2010",
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bibsource = "http://portal.acm.org/;
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@InProceedings{Orlin:2010:IAC,
author = "James B. Orlin",
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clearing prices",
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bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Hartline:2010:BAM,
author = "Jason D. Hartline and Brendan Lucier",
title = "{Bayesian} algorithmic mechanism design",
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pages = "301--310",
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bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Chawla:2010:MPM,
author = "Shuchi Chawla and Jason D. Hartline and David L. Malec
and Balasubramanian Sivan",
title = "Multi-parameter mechanism design and sequential posted
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pages = "311--320",
year = "2010",
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@InProceedings{Lokshtanov:2010:SSA,
author = "Daniel Lokshtanov and Jesper Nederlof",
title = "Saving space by algebraization",
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pages = "321--330",
year = "2010",
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bibsource = "http://portal.acm.org/;
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@InProceedings{Haramaty:2010:SCQ,
author = "Elad Haramaty and Amir Shpilka",
title = "On the structure of cubic and quartic polynomials",
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http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Dasgupta:2010:SJL,
author = "Anirban Dasgupta and Ravi Kumar and Tam{\'a}s Sarlos",
title = "A sparse {Johnson--Lindenstrauss} transform",
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pages = "341--350",
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http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Micciancio:2010:DSE,
author = "Daniele Micciancio and Panagiotis Voulgaris",
title = "A deterministic single exponential time algorithm for
most lattice problems based on {Voronoi} cell
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crossref = "ACM:2010:SPA",
pages = "351--358",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
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acknowledgement = ack-nhfb,
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@InProceedings{Cardinal:2010:SUP,
author = "Jean Cardinal and Samuel Fiorini and Gwena{\"e}l Joret
and Rapha{\"e}l M. Jungers and J. Ian Munro",
title = "Sorting under partial information (without the
ellipsoid algorithm)",
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pages = "359--368",
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bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Lee:2010:MMP,
author = "Jon Lee and Maxim Sviridenko and Jan Vondrak",
title = "Matroid matching: the power of local search",
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pages = "369--378",
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bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Bhattacharya:2010:BCA,
author = "Sayan Bhattacharya and Gagan Goel and Sreenivas
Gollapudi and Kamesh Munagala",
title = "Budget constrained auctions with heterogeneous items",
crossref = "ACM:2010:SPA",
pages = "379--388",
year = "2010",
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bibsource = "http://portal.acm.org/;
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@InProceedings{Fraigniaud:2010:SSW,
author = "Pierre Fraigniaud and George Giakkoupis",
title = "On the searchability of small-world networks with
arbitrary underlying structure",
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pages = "389--398",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
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@InProceedings{Chierichetti:2010:ATB,
author = "Flavio Chierichetti and Silvio Lattanzi and Alessandro
Panconesi",
title = "Almost tight bounds for rumour spreading with
conductance",
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pages = "399--408",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
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@InProceedings{Guruswami:2010:LDR,
author = "Venkatesan Guruswami and Johan H{\aa}stad and Swastik
Kopparty",
title = "On the list-decodability of random linear codes",
crossref = "ACM:2010:SPA",
pages = "409--416",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
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@InProceedings{Kopparty:2010:LLD,
author = "Swastik Kopparty and Shubhangi Saraf",
title = "Local list-decoding and testing of random linear codes
from high error",
crossref = "ACM:2010:SPA",
pages = "417--426",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
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@InProceedings{Meka:2010:PGP,
author = "Raghu Meka and David Zuckerman",
title = "Pseudorandom generators for polynomial threshold
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pages = "427--436",
year = "2010",
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bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
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@InProceedings{Haitner:2010:EIC,
author = "Iftach Haitner and Omer Reingold and Salil Vadhan",
title = "Efficiency improvements in constructing pseudorandom
generators from one-way functions",
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pages = "437--446",
year = "2010",
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@InProceedings{Verbin:2010:LBT,
author = "Elad Verbin and Qin Zhang",
title = "The limits of buffering: a tight lower bound for
dynamic membership in the external memory model",
crossref = "ACM:2010:SPA",
pages = "447--456",
year = "2010",
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@InProceedings{Onak:2010:MLM,
author = "Krzysztof Onak and Ronitt Rubinfeld",
title = "Maintaining a large matching and a small vertex
cover",
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pages = "457--464",
year = "2010",
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@InProceedings{Duan:2010:COF,
author = "Ran Duan and Seth Pettie",
title = "Connectivity oracles for failure prone graphs",
crossref = "ACM:2010:SPA",
pages = "465--474",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
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@InProceedings{Gilbert:2010:ASR,
author = "Anna C. Gilbert and Yi Li and Ely Porat and Martin J.
Strauss",
title = "Approximate sparse recovery: optimizing time and
measurements",
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pages = "475--484",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Godoy:2010:HPD,
author = "Guillem Godoy and Omer Gim{\'e}nez and Lander Ramos
and Carme {\`A}lvarez",
title = "The {HOM} problem is decidable",
crossref = "ACM:2010:SPA",
pages = "485--494",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kawamura:2010:CTO,
author = "Akitoshi Kawamura and Stephen Cook",
title = "Complexity theory for operators in analysis",
crossref = "ACM:2010:SPA",
pages = "495--502",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Burgisser:2010:SPE,
author = "Peter B{\"u}rgisser and Felipe Cucker",
title = "Solving polynomial equations in smoothed polynomial
time and a near solution to {Smale}'s 17th problem",
crossref = "ACM:2010:SPA",
pages = "503--512",
year = "2010",
DOI = "https://doi.org/10.1145/1806689.1806759",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The 17th of the problems proposed by Steve Smale for
the 21st century asks for the existence of a
deterministic algorithm computing an approximate
solution of a system of $n$ complex polynomials in $n$
unknowns in time polynomial, on the average, in the
size $N$ of the input system. A partial solution to
this problem was given by Carlos Beltran and Luis
Miguel Pardo who exhibited a randomized algorithm, call
it LV, doing so. In this paper we further extend this
result in several directions. Firstly, we perform a
smoothed analysis (in the sense of Spielman and Teng)
of algorithm LV and prove that its smoothed complexity
is polynomial in the input size and $\sigma - 1$, where
$\sigma$ controls the size of the random perturbation
of the input systems. Secondly, we perform a
condition-based analysis of LV. That is, we give a
bound, for each system $f$, of the expected running
time of LV with input $f$. In addition to its
dependence on $N$ this bound also depends on the
condition of $f$. Thirdly, and to conclude, we return
to Smale's 17th problem as originally formulated for
deterministic algorithms. We exhibit such an algorithm
and show that its average complexity is $N^{O(\log \log
N)}$. This is nearly a solution to Smale's 17th
problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kuhn:2010:DCD,
author = "Fabian Kuhn and Nancy Lynch and Rotem Oshman",
title = "Distributed computation in dynamic networks",
crossref = "ACM:2010:SPA",
pages = "513--522",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sherstov:2010:OBS,
author = "Alexander A. Sherstov",
title = "Optimal bounds for sign-representing the intersection
of two halfspaces by polynomials",
crossref = "ACM:2010:SPA",
pages = "523--532",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Diakonikolas:2010:BAS,
author = "Ilias Diakonikolas and Prahladh Harsha and Adam
Klivans and Raghu Meka and Prasad Raghavendra and Rocco
A. Servedio and Li-Yang Tan",
title = "Bounding the average sensitivity and noise sensitivity
of polynomial threshold functions",
crossref = "ACM:2010:SPA",
pages = "533--542",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Harsha:2010:IPP,
author = "Prahladh Harsha and Adam Klivans and Raghu Meka",
title = "An invariance principle for polytopes",
crossref = "ACM:2010:SPA",
pages = "543--552",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kalai:2010:ELM,
author = "Adam Tauman Kalai and Ankur Moitra and Gregory
Valiant",
title = "Efficiently learning mixtures of two {Gaussians}",
crossref = "ACM:2010:SPA",
pages = "553--562",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{VAgh:2010:AUN,
author = "L{\'a}szl{\'o} A. V{\'e}gh",
title = "Augmenting undirected node-connectivity by one",
crossref = "ACM:2010:SPA",
pages = "563--572",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Jain:2010:QP,
author = "Rahul Jain and Zhengfeng Ji and Sarvagya Upadhyay and
John Watrous",
title = "{QIP $=$ PSPACE}",
crossref = "ACM:2010:SPA",
pages = "573--582",
year = "2010",
DOI = "https://doi.org/10.1145/1806689.1806768",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove that the complexity class QIP, which consists
of all problems having quantum interactive proof
systems, is contained in PSPACE. This containment is
proved by applying a parallelized form of the matrix
multiplicative weights update method to a class of
semidefinite programs that captures the computational
power of quantum interactive proofs. As the containment
of PSPACE in QIP follows immediately from the
well-known equality IP $=$ PSPACE, the equality QIP $=$
PSPACE follows.",
acknowledgement = ack-nhfb,
remark = "This work won the conference's Best Paper Award. An
updated version appears in Comm. ACM 53(12) 102--109
(December 2010),
\url{https://doi.org/10.1145/1859204.1859231}.",
}
@InProceedings{Byrka:2010:ILB,
author = "Jaroslaw Byrka and Fabrizio Grandoni and Thomas
Rothvo{\ss} and Laura Sanit{\`a}",
title = "An improved {LP}-based approximation for {Steiner}
tree",
crossref = "ACM:2010:SPA",
pages = "583--592",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dodis:2010:CBL,
author = "Yevgeniy Dodis and Mihai Patrascu and Mikkel Thorup",
title = "Changing base without losing space",
crossref = "ACM:2010:SPA",
pages = "593--602",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Patrascu:2010:TPL,
author = "Mihai Patrascu",
title = "Towards polynomial lower bounds for dynamic problems",
crossref = "ACM:2010:SPA",
pages = "603--610",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Fraigniaud:2010:OAS,
author = "Pierre Fraigniaud and Amos Korman",
title = "An optimal ancestry scheme and small universal
posets",
crossref = "ACM:2010:SPA",
pages = "611--620",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lee:2010:BSM,
author = "James R. Lee and Mohammad Moharrami",
title = "Bilipschitz snowflakes and metrics of negative type",
crossref = "ACM:2010:SPA",
pages = "621--630",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Raghavendra:2010:AIS,
author = "Prasad Raghavendra and David Steurer and Prasad
Tetali",
title = "Approximations for the isoperimetric and spectral
profile of graphs and related parameters",
crossref = "ACM:2010:SPA",
pages = "631--640",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Varadarajan:2010:WGS,
author = "Kasturi Varadarajan",
title = "Weighted geometric set cover via quasi-uniform
sampling",
crossref = "ACM:2010:SPA",
pages = "641--648",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Karnin:2010:DIT,
author = "Zohar S. Karnin and Partha Mukhopadhyay and Amir
Shpilka and Ilya Volkovich",
title = "Deterministic identity testing of depth-4 multilinear
circuits with bounded top fan-in",
crossref = "ACM:2010:SPA",
pages = "649--658",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Raz:2010:TRL,
author = "Ran Raz",
title = "Tensor-rank and lower bounds for arithmetic formulas",
crossref = "ACM:2010:SPA",
pages = "659--666",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{HrubeAa:2010:NCC,
author = "Pavel Hrube and Avi Wigderson and Amir Yehudayoff",
title = "Non-commutative circuits and the sum-of-squares
problem",
crossref = "ACM:2010:SPA",
pages = "667--676",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Arvind:2010:HND,
author = "Vikraman Arvind and Srikanth Srinivasan",
title = "On the hardness of the noncommutative determinant",
crossref = "ACM:2010:SPA",
pages = "677--686",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kawarabayashi:2010:SPG,
author = "Ken-ichi Kawarabayashi and Paul Wollan",
title = "A shorter proof of the graph minor algorithm: the
unique linkage theorem",
crossref = "ACM:2010:SPA",
pages = "687--694",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kawarabayashi:2010:OCP,
author = "Ken-ichi Kawarabayashi and Bruce Reed",
title = "Odd cycle packing",
crossref = "ACM:2010:SPA",
pages = "695--704",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hardt:2010:GDP,
author = "Moritz Hardt and Kunal Talwar",
title = "On the geometry of differential privacy",
crossref = "ACM:2010:SPA",
pages = "705--714",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dwork:2010:DPU,
author = "Cynthia Dwork and Moni Naor and Toniann Pitassi and
Guy N. Rothblum",
title = "Differential privacy under continual observation",
crossref = "ACM:2010:SPA",
pages = "715--724",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dyer:2010:CC,
author = "Martin E. Dyer and David M. Richerby",
title = "On the complexity of {\#CSP}",
crossref = "ACM:2010:SPA",
pages = "725--734",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Marx:2010:THP,
author = "D{\'a}niel Marx",
title = "Tractable hypergraph properties for constraint
satisfaction and conjunctive queries",
crossref = "ACM:2010:SPA",
pages = "735--744",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Svensson:2010:CHP,
author = "Ola Svensson",
title = "Conditional hardness of precedence constrained
scheduling on identical machines",
crossref = "ACM:2010:SPA",
pages = "745--754",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Raghavendra:2010:GEU,
author = "Prasad Raghavendra and David Steurer",
title = "Graph expansion and the unique games conjecture",
crossref = "ACM:2010:SPA",
pages = "755--764",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Roth:2010:IPM,
author = "Aaron Roth and Tim Roughgarden",
title = "Interactive privacy via the median mechanism",
crossref = "ACM:2010:SPA",
pages = "765--774",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kasiviswanathan:2010:PPR,
author = "Shiva Prasad Kasiviswanathan and Mark Rudelson and
Adam Smith and Jonathan Ullman",
title = "The price of privately releasing contingency tables
and the spectra of random matrices with correlated
rows",
crossref = "ACM:2010:SPA",
pages = "775--784",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chandran:2010:PAA,
author = "Nishanth Chandran and Bhavana Kanukurthi and Rafail
Ostrovsky and Leonid Reyzin",
title = "Privacy amplification with asymptotically optimal
entropy loss",
crossref = "ACM:2010:SPA",
pages = "785--794",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Akavia:2010:EBO,
author = "Adi Akavia and Oded Goldreich and Shafi Goldwasser and
Dana Moshkovitz",
title = "Erratum for: {{\em On basing one-way functions on
NP-hardness}}",
crossref = "ACM:2010:SPA",
pages = "795--796",
year = "2010",
bibdate = "Wed Sep 1 10:42:57 MDT 2010",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
note = "See \cite{Akavia:2006:BOW}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Patrascu:2011:PST,
author = "Mihai Patrascu and Mikkel Thorup",
title = "The power of simple tabulation hashing",
crossref = "ACM:2011:SPA",
pages = "1--10",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993638",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lenzen:2011:TBP,
author = "Christoph Lenzen and Roger Wattenhofer",
title = "Tight bounds for parallel randomized load balancing:
extended abstract",
crossref = "ACM:2011:SPA",
pages = "11--20",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993639",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Doerr:2011:SNS,
author = "Benjamin Doerr and Mahmoud Fouz and Tobias Friedrich",
title = "Social networks spread rumors in sublogarithmic time",
crossref = "ACM:2011:SPA",
pages = "21--30",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993640",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Regev:2011:QOW,
author = "Oded Regev and Bo'az Klartag",
title = "Quantum one-way communication can be exponentially
stronger than classical communication",
crossref = "ACM:2011:SPA",
pages = "31--40",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993642",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sherstov:2011:SDP,
author = "Alexander A. Sherstov",
title = "Strong direct product theorems for quantum
communication and query complexity",
crossref = "ACM:2011:SPA",
pages = "41--50",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993643",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chakrabarti:2011:OLB,
author = "Amit Chakrabarti and Oded Regev",
title = "An optimal lower bound on the communication complexity
of gap-{Hamming}-distance",
crossref = "ACM:2011:SPA",
pages = "51--60",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993644",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ding:2011:CTB,
author = "Jian Ding and James R. Lee and Yuval Peres",
title = "Cover times, blanket times, and majorizing measures",
crossref = "ACM:2011:SPA",
pages = "61--70",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993646",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Fung:2011:GFG,
author = "Wai Shing Fung and Ramesh Hariharan and Nicholas J. A.
Harvey and Debmalya Panigrahi",
title = "A general framework for graph sparsification",
crossref = "ACM:2011:SPA",
pages = "71--80",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993647",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kawarabayashi:2011:BAA,
author = "Ken-ichi Kawarabayashi and Yusuke Kobayashi",
title = "Breaking $o(n^{1/2})$-approximation algorithms for the
edge-disjoint paths problem with congestion two",
crossref = "ACM:2011:SPA",
pages = "81--88",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993648",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Holenstein:2011:ERO,
author = "Thomas Holenstein and Robin K{\"u}nzler and Stefano
Tessaro",
title = "The equivalence of the random oracle model and the
ideal cipher model, revisited",
crossref = "ACM:2011:SPA",
pages = "89--98",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993650",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gentry:2011:SSN,
author = "Craig Gentry and Daniel Wichs",
title = "Separating succinct non-interactive arguments from all
falsifiable assumptions",
crossref = "ACM:2011:SPA",
pages = "99--108",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993651",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Pass:2011:LPS,
author = "Rafael Pass",
title = "Limits of provable security from standard
assumptions",
crossref = "ACM:2011:SPA",
pages = "109--118",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993652",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Papadimitriou:2011:OSI,
author = "Christos H. Papadimitriou and George Pierrakos",
title = "On optimal single-item auctions",
crossref = "ACM:2011:SPA",
pages = "119--128",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993654",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dobzinski:2011:OAC,
author = "Shahar Dobzinski and Hu Fu and Robert D. Kleinberg",
title = "Optimal auctions with correlated bidders are easy",
crossref = "ACM:2011:SPA",
pages = "129--138",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993655",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dobzinski:2011:IRT,
author = "Shahar Dobzinski",
title = "An impossibility result for truthful combinatorial
auctions with submodular valuations",
crossref = "ACM:2011:SPA",
pages = "139--148",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993656",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dughmi:2011:COR,
author = "Shaddin Dughmi and Tim Roughgarden and Qiqi Yan",
title = "From convex optimization to randomized mechanisms:
toward optimal combinatorial auctions",
crossref = "ACM:2011:SPA",
pages = "149--158",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993657",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Braverman:2011:TCM,
author = "Mark Braverman and Anup Rao",
title = "Towards coding for maximum errors in interactive
communication",
crossref = "ACM:2011:SPA",
pages = "159--166",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993659",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kopparty:2011:HRC,
author = "Swastik Kopparty and Shubhangi Saraf and Sergey
Yekhanin",
title = "High-rate codes with sublinear-time decoding",
crossref = "ACM:2011:SPA",
pages = "167--176",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993660",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Zewi:2011:ATS,
author = "Noga Zewi and Eli Ben-Sasson",
title = "From affine to two-source extractors via approximate
duality",
crossref = "ACM:2011:SPA",
pages = "177--186",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993661",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hatami:2011:CTA,
author = "Hamed Hatami and Shachar Lovett",
title = "Correlation testing for affine invariant properties on
{$\mathbb{F}_p^n$} in the high error regime",
crossref = "ACM:2011:SPA",
pages = "187--194",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993662",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Adsul:2011:RBG,
author = "Bharat Adsul and Jugal Garg and Ruta Mehta and Milind
Sohoni",
title = "Rank-1 bimatrix games: a homeomorphism and a
polynomial time algorithm",
crossref = "ACM:2011:SPA",
pages = "195--204",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993664",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Hansen:2011:EAS,
author = "Kristoffer Arnsfelt Hansen and Michal Koucky and Niels
Lauritzen and Peter Bro Miltersen and Elias P.
Tsigaridas",
title = "Exact algorithms for solving stochastic games:
extended abstract",
crossref = "ACM:2011:SPA",
pages = "205--214",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993665",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Immorlica:2011:DA,
author = "Nicole Immorlica and Adam Tauman Kalai and Brendan
Lucier and Ankur Moitra and Andrew Postlewaite and
Moshe Tennenholtz",
title = "Dueling algorithms",
crossref = "ACM:2011:SPA",
pages = "215--224",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993666",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Moitra:2011:POS,
author = "Ankur Moitra and Ryan O'Donnell",
title = "{Pareto} optimal solutions for smoothed analysts",
crossref = "ACM:2011:SPA",
pages = "225--234",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993667",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kolipaka:2011:MTM,
author = "Kashyap Babu Rao Kolipaka and Mario Szegedy",
title = "{Moser} and {Tardos} meet {Lov{\'a}sz}",
crossref = "ACM:2011:SPA",
pages = "235--244",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993669",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Moser:2011:FDS,
author = "Robin A. Moser and Dominik Scheder",
title = "A full derandomization of {Sch{\"o}ning}'s {$k$-SAT}
algorithm",
crossref = "ACM:2011:SPA",
pages = "245--252",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993670",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gopalan:2011:PGC,
author = "Parikshit Gopalan and Raghu Meka and Omer Reingold and
David Zuckerman",
title = "Pseudorandom generators for combinatorial shapes",
crossref = "ACM:2011:SPA",
pages = "253--262",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993671",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Koucky:2011:PGG,
author = "Michal Kouck{\'y} and Prajakta Nimbhorkar and Pavel
Pudl{\'a}k",
title = "Pseudorandom generators for group products: extended
abstract",
crossref = "ACM:2011:SPA",
pages = "263--272",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993672",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Christiano:2011:EFL,
author = "Paul Christiano and Jonathan A. Kelner and Aleksander
Madry and Daniel A. Spielman and Shang-Hua Teng",
title = "Electrical flows, {Laplacian} systems, and faster
approximation of maximum flow in undirected graphs",
crossref = "ACM:2011:SPA",
pages = "273--282",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993674",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Friedmann:2011:SLB,
author = "Oliver Friedmann and Thomas Dueholm Hansen and Uri
Zwick",
title = "Subexponential lower bounds for randomized pivoting
rules for the simplex algorithm",
crossref = "ACM:2011:SPA",
pages = "283--292",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993675",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Haeupler:2011:ANC,
author = "Bernhard Haeupler",
title = "Analyzing network coding gossip made easy",
crossref = "ACM:2011:SPA",
pages = "293--302",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993676",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chuzhoy:2011:AGC,
author = "Julia Chuzhoy",
title = "An algorithm for the graph crossing number problem",
crossref = "ACM:2011:SPA",
pages = "303--312",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993678",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Italiano:2011:IAM,
author = "Giuseppe F. Italiano and Yahav Nussbaum and Piotr
Sankowski and Christian Wulff-Nilsen",
title = "Improved algorithms for min cut and max flow in
undirected planar graphs",
crossref = "ACM:2011:SPA",
pages = "313--322",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993679",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Dinitz:2011:DSF,
author = "Michael Dinitz and Robert Krauthgamer",
title = "Directed spanners via flow-based linear programs",
crossref = "ACM:2011:SPA",
pages = "323--332",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993680",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Aaronson:2011:CCL,
author = "Scott Aaronson and Alex Arkhipov",
title = "The computational complexity of linear optics",
crossref = "ACM:2011:SPA",
pages = "333--342",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993682",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Brandao:2011:QTA,
author = "Fernando G. S. L. Brand{\~a}o and Matthias Christandl
and Jon Yard",
title = "A quasipolynomial-time algorithm for the quantum
separability problem",
crossref = "ACM:2011:SPA",
pages = "343--352",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993683",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kempe:2011:PRE,
author = "Julia Kempe and Thomas Vidick",
title = "Parallel repetition of entangled games",
crossref = "ACM:2011:SPA",
pages = "353--362",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993684",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sarma:2011:DVH,
author = "Atish Das Sarma and Stephan Holzer and Liah Kor and
Amos Korman and Danupon Nanongkai and Gopal Pandurangan
and David Peleg and Roger Wattenhofer",
title = "Distributed verification and hardness of distributed
approximation",
crossref = "ACM:2011:SPA",
pages = "363--372",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993686",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Golab:2011:LID,
author = "Wojciech Golab and Lisa Higham and Philipp Woelfel",
title = "Linearizable implementations do not suffice for
randomized distributed computation",
crossref = "ACM:2011:SPA",
pages = "373--382",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993687",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kantor:2011:TWC,
author = "Erez Kantor and Zvi Lotker and Merav Parter and David
Peleg",
title = "The topology of wireless communication",
crossref = "ACM:2011:SPA",
pages = "383--392",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993688",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Giakkoupis:2011:OPS,
author = "George Giakkoupis and Nicolas Schabanel",
title = "Optimal path search in small worlds: dimension
matters",
crossref = "ACM:2011:SPA",
pages = "393--402",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993689",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Novocin:2011:LRA,
author = "Andrew Novocin and Damien Stehl{\'e} and Gilles
Villard",
title = "An {LLL}-reduction algorithm with quasi-linear time
complexity: extended abstract",
crossref = "ACM:2011:SPA",
pages = "403--412",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993691",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Khot:2011:NHA,
author = "Subhash Khot and Dana Moshkovitz",
title = "{NP}-hardness of approximately solving linear
equations over reals",
crossref = "ACM:2011:SPA",
pages = "413--420",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993692",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Saraf:2011:BBI,
author = "Shubhangi Saraf and Ilya Volkovich",
title = "Black-box identity testing of depth-4 multilinear
circuits",
crossref = "ACM:2011:SPA",
pages = "421--430",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993693",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Saxena:2011:BIT,
author = "Nitin Saxena and C. Seshadhri",
title = "Blackbox identity testing for bounded top fanin
depth-3 circuits: the field doesn't matter",
crossref = "ACM:2011:SPA",
pages = "431--440",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993694",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Demaine:2011:CDH,
author = "Erik D. Demaine and MohammadTaghi Hajiaghayi and
Ken-ichi Kawarabayashi",
title = "Contraction decomposition in $h$-minor-free graphs and
algorithmic applications",
crossref = "ACM:2011:SPA",
pages = "441--450",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993696",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kawarabayashi:2011:SAS,
author = "Ken-ichi Kawarabayashi and Paul Wollan",
title = "A simpler algorithm and shorter proof for the graph
minor decomposition",
crossref = "ACM:2011:SPA",
pages = "451--458",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993697",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bousquet:2011:MF,
author = "Nicolas Bousquet and Jean Daligault and St{\'e}phan
Thomass{\'e}",
title = "Multicut is {FPT}",
crossref = "ACM:2011:SPA",
pages = "459--468",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993698",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Marx:2011:FPT,
author = "D{\'a}niel Marx and Igor Razgon",
title = "Fixed-parameter tractability of multicut parameterized
by the size of the cutset",
crossref = "ACM:2011:SPA",
pages = "469--478",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993699",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Grohe:2011:FTS,
author = "Martin Grohe and Ken-ichi Kawarabayashi and D{\'a}niel
Marx and Paul Wollan",
title = "Finding topological subgraphs is fixed-parameter
tractable",
crossref = "ACM:2011:SPA",
pages = "479--488",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993700",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kopparty:2011:CPF,
author = "Swastik Kopparty",
title = "On the complexity of powering in finite fields",
crossref = "ACM:2011:SPA",
pages = "489--498",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993702",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Chien:2011:ASH,
author = "Steve Chien and Prahladh Harsha and Alistair Sinclair
and Srikanth Srinivasan",
title = "Almost settling the hardness of noncommutative
determinant",
crossref = "ACM:2011:SPA",
pages = "499--508",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993703",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Burgisser:2011:GCT,
author = "Peter B{\"u}rgisser and Christian Ikenmeyer",
title = "Geometric complexity theory and tensor rank",
crossref = "ACM:2011:SPA",
pages = "509--518",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993704",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Barak:2011:RBD,
author = "Boaz Barak and Zeev Dvir and Amir Yehudayoff and Avi
Wigderson",
title = "Rank bounds for design matrices with applications to
combinatorial geometry and locally correctable codes",
crossref = "ACM:2011:SPA",
pages = "519--528",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993705",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kleinberg:2011:MMA,
author = "Jon Kleinberg and Sigal Oren",
title = "Mechanisms for (mis)allocating scientific credit",
crossref = "ACM:2011:SPA",
pages = "529--538",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993707",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Cole:2011:IPS,
author = "Richard Cole and Jos{\'e} R. Correa and Vasilis
Gkatzelis and Vahab Mirrokni and Neil Olver",
title = "Inner product spaces for {MinSum} coordination
mechanisms",
crossref = "ACM:2011:SPA",
pages = "539--548",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993708",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Feige:2011:MDU,
author = "Uriel Feige and Moshe Tennenholtz",
title = "Mechanism design with uncertain inputs: (to err is
human, to forgive divine)",
crossref = "ACM:2011:SPA",
pages = "549--558",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993709",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Patrascu:2011:DRU,
author = "Mihai P{\u{a}}tra{\c{s}}cu and Mikkel Thorup",
title = "Don't rush into a union: take time to find your
roots",
crossref = "ACM:2011:SPA",
pages = "559--568",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993711",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Feldman:2011:UFA,
author = "Dan Feldman and Michael Langberg",
title = "A unified framework for approximating and clustering
data",
crossref = "ACM:2011:SPA",
pages = "569--578",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993712",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Arya:2011:APM,
author = "Sunil Arya and Guilherme D. da Fonseca and David M.
Mount",
title = "Approximate polytope membership queries",
crossref = "ACM:2011:SPA",
pages = "579--586",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993713",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Karande:2011:OBM,
author = "Chinmay Karande and Aranyak Mehta and Pushkar
Tripathi",
title = "Online bipartite matching with unknown distributions",
crossref = "ACM:2011:SPA",
pages = "587--596",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993715",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Mahdian:2011:OBM,
author = "Mohammad Mahdian and Qiqi Yan",
title = "Online bipartite matching with random arrivals: an
approach based on strongly factor-revealing {LPs}",
crossref = "ACM:2011:SPA",
pages = "597--606",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993716",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Adamaszek:2011:ATB,
author = "Anna Adamaszek and Artur Czumaj and Matthias Englert
and Harald R{\"a}cke",
title = "Almost tight bounds for reordering buffer management",
crossref = "ACM:2011:SPA",
pages = "607--616",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993717",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Svensson:2011:SCS,
author = "Ola Svensson",
title = "{Santa Claus} schedules jobs on unrelated machines",
crossref = "ACM:2011:SPA",
pages = "617--626",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993718",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Indyk:2011:KMC,
author = "Piotr Indyk and Eric Price",
title = "{$K$}-median clustering, model-based compressive
sensing, and sparse recovery for earth mover distance",
crossref = "ACM:2011:SPA",
pages = "627--636",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993720",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bourgain:2011:BBE,
author = "Jean Bourgain and Stephen J. Dilworth and Kevin Ford
and Sergei V. Konyagin and Denka Kutzarova",
title = "Breaking the $k^2$ barrier for explicit {RIP}
matrices",
crossref = "ACM:2011:SPA",
pages = "637--644",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993721",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Karnin:2011:DCH,
author = "Zohar S. Karnin",
title = "Deterministic construction of a high dimensional $l_p$
section in $l_1^n$ for any $p < 2$",
crossref = "ACM:2011:SPA",
pages = "645--654",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993722",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Bodirsky:2011:STG,
author = "Manuel Bodirsky and Michael Pinsker",
title = "{Schaefer}'s theorem for graphs",
crossref = "ACM:2011:SPA",
pages = "655--664",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993724",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Yoshida:2011:OCT,
author = "Yuichi Yoshida",
title = "Optimal constant-time approximation algorithms and
(unconditional) inapproximability results for every
bounded-degree {CSP}",
crossref = "ACM:2011:SPA",
pages = "665--674",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993725",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Newman:2011:EPH,
author = "Ilan Newman and Christian Sohler",
title = "Every property of hyperfinite graphs is testable",
crossref = "ACM:2011:SPA",
pages = "675--684",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993726",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Valiant:2011:EUS,
author = "Gregory Valiant and Paul Valiant",
title = "Estimating the unseen: an $n / \log(n)$-sample
estimator for entropy and support size, shown optimal
via new {CLTs}",
crossref = "ACM:2011:SPA",
pages = "685--694",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993727",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Goyal:2011:CRN,
author = "Vipul Goyal",
title = "Constant round non-malleable protocols using one way
functions",
crossref = "ACM:2011:SPA",
pages = "695--704",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993729",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lin:2011:CRN,
author = "Huijia Lin and Rafael Pass",
title = "Constant-round non-malleable commitments from any
one-way function",
crossref = "ACM:2011:SPA",
pages = "705--714",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993730",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Ajtai:2011:SCI,
author = "Miklos Ajtai",
title = "Secure computation with information leaking to an
adversary",
crossref = "ACM:2011:SPA",
pages = "715--724",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993731",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lewko:2011:HLK,
author = "Allison Lewko and Mark Lewko and Brent Waters",
title = "How to leak on key updates",
crossref = "ACM:2011:SPA",
pages = "725--734",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993732",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Woodruff:2011:NOP,
author = "David P. Woodruff",
title = "Near-optimal private approximation protocols via a
black box transformation",
crossref = "ACM:2011:SPA",
pages = "735--744",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993733",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kane:2011:FME,
author = "Daniel M. Kane and Jelani Nelson and Ely Porat and
David P. Woodruff",
title = "Fast moment estimation in data streams in optimal
space",
crossref = "ACM:2011:SPA",
pages = "745--754",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993735",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Sohler:2011:SEN,
author = "Christian Sohler and David P. Woodruff",
title = "Subspace embeddings for the {$L_1$}-norm with
applications",
crossref = "ACM:2011:SPA",
pages = "755--764",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993736",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lee:2011:NOD,
author = "James R. Lee and Anastasios Sidiropoulos",
title = "Near-optimal distortion bounds for embedding doubling
spaces into {$L_1$}",
crossref = "ACM:2011:SPA",
pages = "765--772",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993737",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Fawzi:2011:LDN,
author = "Omar Fawzi and Patrick Hayden and Pranab Sen",
title = "From low-distortion norm embeddings to explicit
uncertainty relations and efficient information
locking",
crossref = "ACM:2011:SPA",
pages = "773--782",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993738",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Vondrak:2011:SFM,
author = "Jan Vondr{\'a}k and Chandra Chekuri and Rico
Zenklusen",
title = "Submodular function maximization via the multilinear
relaxation and contention resolution schemes",
crossref = "ACM:2011:SPA",
pages = "783--792",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993740",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Balcan:2011:LSF,
author = "Maria-Florina Balcan and Nicholas J. A. Harvey",
title = "Learning submodular functions",
crossref = "ACM:2011:SPA",
pages = "793--802",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993741",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Gupta:2011:PRC,
author = "Anupam Gupta and Moritz Hardt and Aaron Roth and
Jonathan Ullman",
title = "Privately releasing conjunctions and the statistical
query barrier",
crossref = "ACM:2011:SPA",
pages = "803--812",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993742",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Smith:2011:PPS,
author = "Adam Smith",
title = "Privacy-preserving statistical estimation with optimal
convergence rates",
crossref = "ACM:2011:SPA",
pages = "813--822",
year = "2011",
DOI = "https://doi.org/10.1145/1993636.1993743",
bibdate = "Tue Jun 7 18:53:27 MDT 2011",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Kelner:2012:FAM,
author = "Jonathan A. Kelner and Gary L. Miller and Richard
Peng",
title = "Faster approximate multicommodity flow using
quadratically coupled flows",
crossref = "ACM:2012:SPA",
pages = "1--18",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213979",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The maximum multicommodity flow problem is a natural
generalization of the maximum flow problem to route
multiple distinct flows. Obtaining a $1 - \epsilon$
approximation to the multicommodity flow problem on
graphs is a well-studied problem. In this paper we
present an adaptation of recent advances in
single-commodity flow algorithms to this problem. As
the underlying linear systems in the electrical
problems of multicommodity flow problems are no longer
Laplacians, our approach is tailored to generate
specialized systems which can be preconditioned and
solved efficiently using Laplacians. Given an
undirected graph with $m$ edges and $k$ commodities, we
give algorithms that find $1 - \epsilon$ approximate
solutions to the maximum concurrent flow problem and
maximum weighted multicommodity flow problem in time
$O(m^{4/3} \poly(k, \epsilon^{-1}))$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chakrabarti:2012:WCC,
author = "Amit Chakrabarti and Lisa Fleischer and Christophe
Weibel",
title = "When the cut condition is enough: a complete
characterization for multiflow problems in
series-parallel networks",
crossref = "ACM:2012:SPA",
pages = "19--26",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213980",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Let $G = (V, E)$ be a supply graph and $H = (V,F)$ a
demand graph defined on the same set of vertices. An
assignment of capacities to the edges of $G$ and
demands to the edges of $H$ is said to satisfy the cut
condition if for any cut in the graph, the total demand
crossing the cut is no more than the total capacity
crossing it. The pair $(G, H)$ is called cut-sufficient
if for any assignment of capacities and demands that
satisfy the cut condition, there is a multiflow routing
the demands defined on $H$ within the network with
capacities defined on $G$. We prove a previous
conjecture, which states that when the supply graph $G$
is series-parallel, the pair (G,H) is cut-sufficient if
and only if $(G, H)$ does not contain an odd spindle as
a minor; that is, if it is impossible to contract edges
of $G$ and delete edges of $G$ and $H$ so that $G$
becomes the complete bipartite graph $K_{2,p}$, with $p
\geq 3$ odd, and $H$ is composed of a cycle connecting
the $p$ vertices of degree $2$, and an edge connecting
the two vertices of degree $p$. We further prove that
if the instance is Eulerian --- that is, the demands
and capacities are integers and the total of demands
and capacities incident to each vertex is even --- then
the multiflow problem has an integral solution. We
provide a polynomial-time algorithm to find an integral
solution in this case. In order to prove these results,
we formulate properties of tight cuts (cuts for which
the cut condition inequality is tight) in
cut-sufficient pairs. We believe these properties might
be useful in extending our results to planar graphs.",
acknowledgement = ack-nhfb,
}
@InProceedings{Vegh:2012:SPA,
author = "L{\'a}szl{\'o} A. V{\'e}gh",
title = "Strongly polynomial algorithm for a class of
minimum-cost flow problems with separable convex
objectives",
crossref = "ACM:2012:SPA",
pages = "27--40",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213981",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A well-studied nonlinear extension of the minimum-cost
flow problem is to minimize the objective $\Sigma_{i j
\in E} C_{ij} (f_{ij})$ over feasible flows $f$, where
on every arc $ij$ of the network, $C_{ij}$ is a convex
function. We give a strongly polynomial algorithm for
finding an exact optimal solution for a broad class of
such problems. The key characteristic of this class is
that an optimal solution can be computed exactly
provided its support. This includes separable convex
quadratic objectives and also certain market equilibria
problems: Fisher's market with linear and with spending
constraint utilities. We thereby give the first
strongly polynomial algorithms for separable quadratic
minimum-cost flows and for Fisher's market with
spending constraint utilities, settling open questions
posed e.g. in [15] and in [35], respectively. The
running time is $O(m^4 \log m)$ for quadratic costs,
$O(n^4 + n^2 (m + n \log n) \log n)$ for Fisher's
markets with linear utilities and $O(m n^3 + m^2 (m + n
\log n) \log m)$ for spending constraint utilities.",
acknowledgement = ack-nhfb,
}
@InProceedings{Aaronson:2012:QMH,
author = "Scott Aaronson and Paul Christiano",
title = "Quantum money from hidden subspaces",
crossref = "ACM:2012:SPA",
pages = "41--60",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213983",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Forty years ago, Wiesner pointed out that quantum
mechanics raises the striking possibility of money that
cannot be counterfeited according to the laws of
physics. We propose the first quantum money scheme that
is (1) public-key --- meaning that anyone can verify a
banknote as genuine, not only the bank that printed it,
and (2) cryptographically secure, under a ``classical''
hardness assumption that has nothing to do with quantum
money. Our scheme is based on hidden subspaces, encoded
as the zero-sets of random multivariate polynomials. A
main technical advance is to show that the
``black-box'' version of our scheme, where the
polynomials are replaced by classical oracles, is
unconditionally secure. Previously, such a result had
only been known relative to a quantum oracle (and even
there, the proof was never published). Even in
Wiesner's original setting --- quantum money that can
only be verified by the bank --- we are able to use our
techniques to patch a major security hole in Wiesner's
scheme. We give the first private-key quantum money
scheme that allows unlimited verifications and that
remains unconditionally secure, even if the
counterfeiter can interact adaptively with the bank.
Our money scheme is simpler than previous public-key
quantum money schemes, including a knot-based scheme of
Farhi et al. The verifier needs to perform only two
tests, one in the standard basis and one in the
Hadamard basis --- matching the original intuition for
quantum money, based on the existence of complementary
observables. Our security proofs use a new variant of
Ambainis's quantum adversary method, and several other
tools that might be of independent interest.",
acknowledgement = ack-nhfb,
}
@InProceedings{Vazirani:2012:CQD,
author = "Umesh Vazirani and Thomas Vidick",
title = "Certifiable quantum dice: or, true random number
generation secure against quantum adversaries",
crossref = "ACM:2012:SPA",
pages = "61--76",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213984",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We introduce a protocol through which a pair of
quantum mechanical devices may be used to generate $n$
bits that are $\epsilon$-close in statistical distance
from $n$ uniformly distributed bits, starting from a
seed of $O(\log n \log 1 / \epsilon)$ uniform bits. The
bits generated are certifiably random based only on a
simple statistical test that can be performed by the
user, and on the assumption that the devices do not
communicate in the middle of each phase of the
protocol. No other assumptions are placed on the
devices' inner workings. A modified protocol uses a
seed of $O(\log^3 n)$ uniformly random bits to generate
$n$ bits that are $\poly^{-1}(n)$-indistinguishable
from uniform even from the point of view of a quantum
adversary who may have had prior access to the devices,
and may be entangled with them.",
acknowledgement = ack-nhfb,
}
@InProceedings{Belovs:2012:SPF,
author = "Aleksandrs Belovs",
title = "Span programs for functions with constant-sized
$1$-certificates: extended abstract",
crossref = "ACM:2012:SPA",
pages = "77--84",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213985",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Besides the Hidden Subgroup Problem, the second large
class of quantum speed-ups is for functions with
constant-sized 1-certificates. This includes the OR
function, solvable by the Grover algorithm, the element
distinctness, the triangle and other problems. The
usual way to solve them is by quantum walk on the
Johnson graph. We propose a solution for the same
problems using span programs. The span program is a
computational model equivalent to the quantum query
algorithm in its strength, and yet very different in
its outfit. We prove the power of our approach by
designing a quantum algorithm for the triangle problem
with query complexity $O(n^{35/27})$ that is better
than $O(n^{13/10})$ of the best previously known
algorithm by Magniez et al.",
acknowledgement = ack-nhfb,
}
@InProceedings{Larsen:2012:CPC,
author = "Kasper Green Larsen",
title = "The cell probe complexity of dynamic range counting",
crossref = "ACM:2012:SPA",
pages = "85--94",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213987",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In this paper we develop a new technique for proving
lower bounds on the update time and query time of
dynamic data structures in the cell probe model. With
this technique, we prove the highest lower bound to
date for any explicit problem, namely a lower bound of
$t_q = \Omega((\lg n / \lg (wt_u))^2)$. Here $n$ is the
number of update operations, $w$ the cell size, $t_q$
the query time and t$_u$ the update time. In the most
natural setting of cell size $w = \Theta(\lg n)$, this
gives a lower bound of $t_q = \Omega((\lg n / \lg \lg
n)^2)$ for any polylogarithmic update time. This bound
is almost a quadratic improvement over the highest
previous lower bound of $\Omega(\lg n)$, due to
Patrascu and Demaine [SICOMP'06]. We prove our lower
bound for the fundamental problem of weighted
orthogonal range counting. In this problem, we are to
support insertions of two-dimensional points, each
assigned a $\Theta(\lg n)$-bit integer weight. A query
to this problem is specified by a point $q = (x, y)$,
and the goal is to report the sum of the weights
assigned to the points dominated by $q$, where a point
$(x',y')$ is dominated by $q$ if $x' \leq x$ and $y'
\leq y$. In addition to being the highest cell probe
lower bound to date, our lower bound is also tight for
data structures with update time $t_u = \Omega(\lg^{2 +
\epsilon} n)$, where $\epsilon > 0$ is an arbitrarily
small constant.",
acknowledgement = ack-nhfb,
}
@InProceedings{Fiorini:2012:LVS,
author = "Samuel Fiorini and Serge Massar and Sebastian Pokutta
and Hans Raj Tiwary and Ronald de Wolf",
title = "Linear vs. semidefinite extended formulations:
exponential separation and strong lower bounds",
crossref = "ACM:2012:SPA",
pages = "95--106",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213988",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We solve a 20-year old problem posed by Yannakakis and
prove that there exists no polynomial-size linear
program (LP) whose associated polytope projects to the
traveling salesman polytope, even if the LP is not
required to be symmetric. Moreover, we prove that this
holds also for the cut polytope and the stable set
polytope. These results were discovered through a new
connection that we make between one-way quantum
communication protocols and semidefinite programming
reformulations of LPs.",
acknowledgement = ack-nhfb,
}
@InProceedings{Goel:2012:PCA,
author = "Gagan Goel and Vahab Mirrokni and Renato Paes Leme",
title = "Polyhedral clinching auctions and the {AdWords}
polytope",
crossref = "ACM:2012:SPA",
pages = "107--122",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213990",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A central issue in applying auction theory in practice
is the problem of dealing with budget-constrained
agents. A desirable goal in practice is to design
incentive compatible, individually rational, and Pareto
optimal auctions while respecting the budget
constraints. Achieving this goal is particularly
challenging in the presence of nontrivial combinatorial
constraints over the set of feasible allocations.
Toward this goal and motivated by AdWords auctions, we
present an auction for polymatroidal environments
satisfying the above properties. Our auction employs a
novel clinching technique with a clean geometric
description and only needs an oracle access to the
submodular function defining the polymatroid. As a
result, this auction not only simplifies and
generalizes all previous results, it applies to several
new applications including AdWords Auctions, bandwidth
markets, and video on demand. In particular, our
characterization of the AdWords auction as
polymatroidal constraints might be of independent
interest. This allows us to design the first mechanism
for Ad Auctions taking into account simultaneously
budgets, multiple keywords and multiple slots. We show
that it is impossible to extend this result to generic
polyhedral constraints. This also implies an
impossibility result for multi-unit auctions with
decreasing marginal utilities in the presence of budget
constraints.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kleinberg:2012:MPI,
author = "Robert Kleinberg and Seth Matthew Weinberg",
title = "Matroid prophet inequalities",
crossref = "ACM:2012:SPA",
pages = "123--136",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213991",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Consider a gambler who observes a sequence of
independent, non-negative random numbers and is allowed
to stop the sequence at any time, claiming a reward
equal to the most recent observation. The famous
prophet inequality of Krengel, Sucheston, and Garling
asserts that a gambler who knows the distribution of
each random variable can achieve at least half as much
reward, in expectation, as a ``prophet'' who knows the
sampled values of each random variable and can choose
the largest one. We generalize this result to the
setting in which the gambler and the prophet are
allowed to make more than one selection, subject to a
matroid constraint. We show that the gambler can still
achieve at least half as much reward as the prophet;
this result is the best possible, since it is known
that the ratio cannot be improved even in the original
prophet inequality, which corresponds to the special
case of rank-one matroids. Generalizing the result
still further, we show that under an intersection of
$p$ matroid constraints, the prophet's reward exceeds
the gambler's by a factor of at most $O(p)$, and this
factor is also tight. Beyond their interest as theorems
about pure online algorithms or optimal stopping rules,
these results also have applications to mechanism
design. Our results imply improved bounds on the
ability of sequential posted-price mechanisms to
approximate optimal mechanisms in both single-parameter
and multi-parameter Bayesian settings. In particular,
our results imply the first efficiently computable
constant-factor approximations to the Bayesian optimal
revenue in certain multi-parameter settings.",
acknowledgement = ack-nhfb,
}
@InProceedings{Devanur:2012:OMC,
author = "Nikhil R. Devanur and Kamal Jain",
title = "Online matching with concave returns",
crossref = "ACM:2012:SPA",
pages = "137--144",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213992",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider a significant generalization of the
AdWords problem by allowing arbitrary concave returns,
and we characterize the optimal competitive ratio
achievable. The problem considers a sequence of items
arriving online that have to be allocated to agents,
with different agents bidding different amounts. The
objective function is the sum, over each agent i, of a
monotonically non-decreasing concave function $M_i: R_?
+ \to R_+$ of the total amount allocated to $i$. All
variants of online matching problems (including the
AdWords problem) studied in the literature consider the
special case of budgeted linear functions, that is,
functions of the form $M_i(u_i) = \min\{u_i, B_i\}$ for
some constant $B_i$. The distinguishing feature of this
paper is in allowing arbitrary concave returns. The
main result of this paper is that for each concave
function $M$, there exists a constant $F(M) \leq 1$
such that: there exists an algorithm with competitive
ratio of $\min_i F(M_i)$, independent of the sequence
of items. No algorithm has a competitive ratio larger
than $F(M)$ over all instances with $M_i = M$ for all
$i$. Our algorithm is based on the primal-dual paradigm
and makes use of convex programming duality. The upper
bounds are obtained by formulating the task of finding
the right counterexample as an optimization problem.
This path takes us through the calculus of variations
which deals with optimizing over continuous functions.
The algorithm and the upper bound are related to each
other via a set of differential equations, which points
to a certain kind of duality between them.",
acknowledgement = ack-nhfb,
}
@InProceedings{Arora:2012:CNM,
author = "Sanjeev Arora and Rong Ge and Ravindran Kannan and
Ankur Moitra",
title = "Computing a nonnegative matrix factorization ---
provably",
crossref = "ACM:2012:SPA",
pages = "145--162",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213994",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The Nonnegative Matrix Factorization (NMF) problem has
a rich history spanning quantum mechanics, probability
theory, data analysis, polyhedral combinatorics,
communication complexity, demography, chemometrics,
etc. In the past decade NMF has become enormously
popular in machine learning, where the factorization is
computed using a variety of local search heuristics.
Vavasis recently proved that this problem is
NP-complete. We initiate a study of when this problem
is solvable in polynomial time. Consider a nonnegative
$m \times n$ matrix $M$ and a target inner-dimension
$r$. Our results are the following: --- We give a
polynomial-time algorithm for exact and approximate NMF
for every constant $r$. Indeed NMF is most interesting
in applications precisely when $r$ is small. We
complement this with a hardness result, that if exact
NMF can be solved in time $(n m)^{o(r)}$, 3-SAT has a
sub-exponential time algorithm. Hence, substantial
improvements to the above algorithm are unlikely. ---
We give an algorithm that runs in time polynomial in n,
$m$ and $r$ under the separability condition identified
by Donoho and Stodden in 2003. The algorithm may be
practical since it is simple and noise tolerant (under
benign assumptions). Separability is believed to hold
in many practical settings. To the best of our
knowledge, this last result is the first
polynomial-time algorithm that provably works under a
non-trivial condition on the input matrix and we
believe that this will be an interesting and important
direction for future work.",
acknowledgement = ack-nhfb,
}
@InProceedings{Forbes:2012:ITT,
author = "Michael A. Forbes and Amir Shpilka",
title = "On identity testing of tensors, low-rank recovery and
compressed sensing",
crossref = "ACM:2012:SPA",
pages = "163--172",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213995",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the problem of obtaining efficient,
deterministic, {\em black-box polynomial identity
testing algorithms\/} for depth-$3$ set-multilinear
circuits (over arbitrary fields). This class of
circuits has an efficient, deterministic, white-box
polynomial identity testing algorithm (due to Raz and
Shpilka [36]), but has no known such black-box
algorithm. We recast this problem as a question of
finding a low-dimensional subspace $H$, spanned by rank
$1$ tensors, such that any non-zero tensor in the dual
space $\ker(H)$ has high rank. We obtain explicit
constructions of essentially optimal-size hitting sets
for tensors of degree $2$ (matrices), and obtain the
first quasi-polynomial sized hitting sets for arbitrary
tensors.\par
We also show connections to the task of performing
low-rank recovery of matrices, which is studied in the
field of compressed sensing. Low-rank recovery asks
(say, over $R$) to recover a matrix $M$ from few
measurements, under the promise that $M$ is rank $\leq
r$. In this work, we restrict our attention to
recovering matrices that are exactly rank $\leq r$
using deterministic, non-adaptive, linear measurements,
that are free from noise. Over $R$, we provide a set
(of size $4 n r$) of such measurements, from which $M$
can be recovered in $O(r n^2 + r^3 n)$ field
operations, and the number of measurements is
essentially optimal. Further, the measurements can be
taken to be all rank-$1$ matrices, or all sparse
matrices. To the best of our knowledge no explicit
constructions with those properties were known prior to
this work.\par
We also give a more formal connection between low-rank
recovery and the task of {\em sparse (vector)
recovery\/}: any sparse-recovery algorithm that exactly
recovers vectors of length $n$ and sparsity $2 r$,
using $m$ non-adaptive measurements, yields a low-rank
recovery scheme for exactly recovering $n \times n$
matrices of rank $\leq r$, making $2 n m$ non-adaptive
measurements. Furthermore, if the sparse-recovery
algorithm runs in time $\tau$, then the low-rank
recovery algorithm runs in time $O(r n^2 + n \tau)$. We
obtain this reduction using linear-algebraic
techniques, and not using convex optimization, which is
more commonly seen in compressed sensing
algorithms.\par
Finally, we also make a connection to {\em rank-metric
codes}, as studied in coding theory. These are codes
with codewords consisting of matrices (or tensors)
where the distance of matrices $M$ and $N$ is rank $(M
- N)$, as opposed to the usual Hamming metric. We
obtain essentially optimal-rate codes over matrices,
and provide an efficient decoding algorithm. We obtain
codes over tensors as well, with poorer rate, but still
with efficient decoding.",
acknowledgement = ack-nhfb,
}
@InProceedings{Grohe:2012:STI,
author = "Martin Grohe and D{\'a}niel Marx",
title = "Structure theorem and isomorphism test for graphs with
excluded topological subgraphs",
crossref = "ACM:2012:SPA",
pages = "173--192",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213996",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We generalize the structure theorem of Robertson and
Seymour for graphs excluding a fixed graph $H$ as a
minor to graphs excluding $H$ as a topological
subgraph. We prove that for a fixed H, every graph
excluding $H$ as a topological subgraph has a tree
decomposition where each part is either ``almost
embeddable'' to a fixed surface or has bounded degree
with the exception of a bounded number of vertices.
Furthermore, such a decomposition is computable by an
algorithm that is fixed-parameter tractable with
parameter $|H|$. We present two algorithmic
applications of our structure theorem. To illustrate
the mechanics of a ``typical'' application of the
structure theorem, we show that on graphs excluding $H$
as a topological subgraph, Partial Dominating Set (find
$k$ vertices whose closed neighborhood has maximum
size) can be solved in time $f(H,k) \cdot n^{O(1)}$
time. More significantly, we show that on graphs
excluding $H$ as a topological subgraph, Graph
Isomorphism can be solved in time $n^{f(H)}$. This
result unifies and generalizes two previously known
important polynomial-time solvable cases of Graph
Isomorphism: bounded-degree graphs and H-minor free
graphs. The proof of this result needs a generalization
of our structure theorem to the context of invariant
treelike decomposition.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hrubes:2012:SPD,
author = "Pavel Hrubes and Iddo Tzameret",
title = "Short proofs for the determinant identities",
crossref = "ACM:2012:SPA",
pages = "193--212",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213998",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study arithmetic proof systems $P_c(F)$ and
$P_f(F)$ operating with arithmetic circuits and
arithmetic formulas, respectively, that prove
polynomial identities over a field $F$. We establish a
series of structural theorems about these proof
systems, the main one stating that $P_c(F)$ proofs can
be balanced: if a polynomial identity of syntactic
degree $d$ and depth $k$ has a $P_c(F)$ proof of size
$s$, then it also has a $P_c(F)$ proof of size
$\poly(s,d)$ and depth $O(k + \log^2 d + \log d \cdot
\log s)$. As a corollary, we obtain a quasipolynomial
simulation of $P_c(F)$ by $P_f(F)$, for identities of a
polynomial syntactic degree.\par
Using these results we obtain the following: consider
the identities:\par
$$\det(X Y) = \det(X) \cdot \det(Y) \quad {\rm and}
\quad \det(Z) = z_{11} \cdots z_{nn},$$\par
where $X$, $Y$ and $Z$ are $n \times n$ square matrices
and $Z$ is a triangular matrix with $z_{11}, \ldots{},
z_{nn}$ on the diagonal (and $\det$ is the determinant
polynomial). Then we can construct a polynomial-size
arithmetic circuit $\det$ such that the above
identities have $P_c(F)$ proofs of polynomial-size and
$O(\log^2 n)$ depth. Moreover, there exists an
arithmetic formula det of size $n^{O(\log n)}$ such
that the above identities have $P_f(F)$ proofs of size
$n^{O(\log n)}$.\par
This yields a solution to a basic open problem in
propositional proof complexity, namely, whether there
are polynomial-size NC$^2$-Frege proofs for the
determinant identities and the hard matrix identities,
as considered, e.g. in Soltys and Cook (2004) (cf.,
Beame and Pitassi (1998)). We show that matrix
identities like $A B = I \to B A = I$ (for matrices
over the two element field) as well as basic properties
of the determinant have polynomial-size NC$^2$-Frege
proofs, and quasipolynomial-size Frege proofs.",
acknowledgement = ack-nhfb,
}
@InProceedings{Beame:2012:TST,
author = "Paul Beame and Christopher Beck and Russell
Impagliazzo",
title = "Time-space tradeoffs in resolution: superpolynomial
lower bounds for superlinear space",
crossref = "ACM:2012:SPA",
pages = "213--232",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2213999",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give the first time-space tradeoff lower bounds for
Resolution proofs that apply to superlinear space. In
particular, we show that there are formulas of size $N$
that have Resolution refutations of space and size each
roughly $N^{\log 2 N}$ (and like all formulas have
Resolution refutations of space $N$) for which any
Resolution refutation using space $S$ and length $T$
requires $T \geq (N^{0.58 \log 2 N} /S)^{\Omega(\log
\log N/\log \log \log N)}$. By downward translation, a
similar tradeoff applies to all smaller space bounds.
We also show somewhat stronger time-space tradeoff
lower bounds for Regular Resolution, which are also the
first to apply to superlinear space. Namely, for any
space bound $S$ at most $2^{o(N^{1/4})}$ there are
formulas of size $N$, having clauses of width $4$, that
have Regular Resolution proofs of space $S$ and
slightly larger size $T = O(NS)$, but for which any
Regular Resolution proof of space $S^{1 - \epsilon}$
requires length $T^{\Omega(\log \log N / \log \log \log
N)}$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Huynh:2012:VSP,
author = "Trinh Huynh and Jakob Nordstrom",
title = "On the virtue of succinct proofs: amplifying
communication complexity hardness to time-space
trade-offs in proof complexity",
crossref = "ACM:2012:SPA",
pages = "233--248",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214000",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "An active line of research in proof complexity over
the last decade has been the study of proof space and
trade-offs between size and space. Such questions were
originally motivated by practical SAT solving, but have
also led to the development of new theoretical concepts
in proof complexity of intrinsic interest and to
results establishing nontrivial relations between space
and other proof complexity measures. By now, the
resolution proof system is fairly well understood in
this regard, as witnessed by a sequence of papers
leading up to [Ben-Sasson and Nordstrom 2008, 2011] and
[Beame, Beck, and Impagliazzo 2012]. However, for other
relevant proof systems in the context of SAT solving,
such as polynomial calculus (PC) and cutting planes
(CP), very little has been known. Inspired by [BN08,
BN11], we consider CNF encodings of so-called pebble
games played on graphs and the approach of making such
pebbling formulas harder by simple syntactic
modifications. We use this paradigm of hardness
amplification to make progress on the relatively
longstanding open question of proving time-space
trade-offs for PC and CP. Namely, we exhibit a family
of modified pebbling formulas $\{F_n\}$ such that: ---
The formulas $F_n$ have size $O(n)$ and width $O(1)$.
--- They have proofs in length $O(n)$ in resolution,
which generalize to both PC and CP. --- Any refutation
in CP or PCR (a generalization of PC) in length $L$ and
space $s$ must satisfy $s \log L > \approx \sqrt
[4]{n}$. A crucial technical ingredient in these
results is a new two-player communication complexity
lower bound for composed search problems in terms of
block sensitivity, a contribution that we believe to be
of independent interest.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ajtai:2012:DVN,
author = "Mikl{\'o}s Ajtai",
title = "Determinism versus nondeterminism with arithmetic
tests and computation: extended abstract",
crossref = "ACM:2012:SPA",
pages = "249--268",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214001",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "For each natural number $d$ we consider a finite
structure $M_d$ whose universe is the set of all $0,
1$-sequence of length $n = 2^d$, each representing a
natural number in the set $\{0, 1, \ldots{}, 2^n - 1\}$
in binary form. The operations included in the
structure are the four constants $0$, $1$, $2^n - 1$,
$n$, multiplication and addition modulo $2^n$, the
unary function $\min\{2^x, 2^n - 1\}$, the binary
functions $\lfloor x / y \rfloor$ (with $\lfloor x / 0
\rfloor = 0$), $\max(x, y)$, $\min(x, y)$, and the
boolean vector operations $\wedge$, $\vee$, [??not??]
defined on $0, 1$ sequences of length $n$ by performing
the operations on all components simultaneously. These
are essentially the arithmetic operations that can be
performed on a RAM, with wordlength $n$, by a single
instruction. We show that there exists a term (that is,
an algebraic expression) $F(x,y)$ built up from the
mentioned operations, with the only free variables $x$,
$y$, such that for all terms $G(y)$, which is also
built up from the mentioned operations, the following
holds. For infinitely many positive integers $d$, there
exists an $a \in M_d$ such that the following two
statements are not equivalent: (i) $M_d \models \exists
x, F(x,a)$, (ii) $M_d \models G(a) = 0$. In other
words, the question whether an existential statement,
depending on the parameter $a \in M_d$ is true or not,
cannot be decided by evaluating an algebraic expression
at $a$.\par
Another way of formulating the theorem, in a slightly
stronger form, is, that over the structures $M_d$,
quantifier elimination is not possible in the following
sense. Let $\cal M$ be a first-order language with
equality, containing function symbols for all of the
mentioned arithmetic operations. Then there exists an
existential first-order formula $\phi(y)$ of $\cal M$,
containing a single existential quantifier and the only
free variable $y$, such that for each propositional
formula $P(y)$ of $\cal M$, we have that for infinitely
many positive integers $d$, $\phi(y)$ and $P(y)$ are
not equivalent on $M_d$, that is, $M_d \models {\em
[not]} \forall y$, $\phi(y) \leftrightarrow
P(y)$.\par
We also show that the theorem, in both forms, remains
true if the binary operation $\min\{x^y, 2^n - 1\}$ is
added to the structure $M_d$. A general theorem is
proved as well, which describes sufficient conditions
for a set of operations on a sequence of structures
$K_d$, $d = 1, 2, \ldots{}$ which guarantees that the
analogues of the mentioned theorems holds for the
structures $K_d$ too.",
acknowledgement = ack-nhfb,
}
@InProceedings{Heilman:2012:SPC,
author = "Steven Heilman and Aukosh Jagannath and Assaf Naor",
title = "Solution of the propeller conjecture in
{$\mathbb{R}^3$}",
crossref = "ACM:2012:SPA",
pages = "269--276",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214003",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "It is shown that every measurable partition $\{A_1,
\ldots{}, A_k\}$ of $\mathbb{R}^3$
satisfies:\par
$$\sum_{i = 1}^k || \int_{A i} x e^{-1/2||x||^2_2} \,
dx||_2^2 \leq 9 \pi ^2$$.\par
Let $\{P_1, P_2, P_3\}$ be the partition of
$\mathbb{R}^2$ into $120^\circ$ sectors centered at the
origin. The bound (1) is sharp, with equality holding
if $A_i = P_i \times \mathbb{R}$ for $i \in \{1, 2,
3\}$ and $A_i = \emptyset$ for $i \in \{4, \ldots{},
k\}$. This settles positively the 3-dimensional
Propeller Conjecture of Khot and Naor (FOCS 2008). The
proof of (1) reduces the problem to a finite set of
numerical inequalities which are then verified with
full rigor in a computer-assisted fashion. The main
consequence (and motivation) of (1) is
complexity-theoretic: the Unique Games hardness
threshold of the Kernel Clustering problem with $4
\times 4$ centered and spherical hypothesis matrix
equals $2 \pi /3$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Khot:2012:LHC,
author = "Subhash A. Khot and Preyas Popat and Nisheeth K.
Vishnoi",
title = "$2^{\log^{1 - \epsilon} n}$ hardness for the closest
vector problem with preprocessing",
crossref = "ACM:2012:SPA",
pages = "277--288",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214004",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove that for an arbitrarily small constant
$\epsilon > 0$, assuming NP $\not\subseteq$ DTIME
$(2^{\log^{O(1 / \epsilon) n}})$, the preprocessing
versions of the closest vector problem and the nearest
codeword problem are hard to approximate within a
factor better than $2^{\log^{1 - \epsilon} n}$. This
improves upon the previous hardness factor of $(\log
n)^\delta$ for some $\delta > 0$ due to [AKKV05].",
acknowledgement = ack-nhfb,
}
@InProceedings{ODonnell:2012:NPN,
author = "Ryan O'Donnell and John Wright",
title = "A new point of {NP}-hardness for unique games",
crossref = "ACM:2012:SPA",
pages = "289--306",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214005",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We show that distinguishing $1/2$-satisfiable
Unique-Games instances from $(3/8 +
\epsilon)$-satisfiable instances is NP-hard (for all
$\epsilon > 0$). A consequence is that we match or
improve the best known $c$ vs. $s$ NP-hardness result
for Unique-Games for all values of $c$ (except for $c$
very close to $0$). For these $c$, ours is the first
hardness result showing that it helps to take the
alphabet size larger than $2$. Our NP-hardness
reductions are quasilinear-size and thus show nearly
full exponential time is required, assuming the ETH.",
acknowledgement = ack-nhfb,
}
@InProceedings{Barak:2012:HSS,
author = "Boaz Barak and Fernando G. S. L. Brandao and Aram W.
Harrow and Jonathan Kelner and David Steurer and Yuan
Zhou",
title = "Hypercontractivity, sum-of-squares proofs, and their
applications",
crossref = "ACM:2012:SPA",
pages = "307--326",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214006",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the computational complexity of approximating
the $2$-to-$q$ norm of linear operators (defined as
$||A||_{2 \to q} = \max_{v \neq 0} ||A v||_q /
||v||_2$) for $q > 2$, as well as connections between
this question and issues arising in quantum information
theory and the study of Khot's Unique Games Conjecture
(UGC). We show the following: For any constant even
integer $q \geq 4$, a graph $G$ is a small-set expander
if and only if the projector into the span of the top
eigenvectors of $G$'s adjacency matrix has bounded $2
\to q$ norm. As a corollary, a good approximation to
the $2 \to q$ norm will refute the Small-Set Expansion
Conjecture --- a close variant of the UGC. We also show
that such a good approximation can be obtained in
$\exp(n^{2 / q})$ time, thus obtaining a different
proof of the known subexponential algorithm for
Small-Set-Expansion. Constant rounds of the ``Sum of
Squares'' semidefinite programming hierarchy certify an
upper bound on the $2 \to 4$ norm of the projector to
low degree polynomials over the Boolean cube, as well
certify the unsatisfiability of the ``noisy cube'' and
``short code'' based instances of Unique-Games
considered by prior works. This improves on the
previous upper bound of $\exp(\log^{O(1)} n)$ rounds
(for the ``short code''), as well as separates the
``Sum of Squares'' / ``Lasserre'' hierarchy from weaker
hierarchies that were known to require $\omega(1)$
rounds. We show reductions between computing the $2 \to
4$ norm and computing the injective tensor norm of a
tensor, a problem with connections to quantum
information theory. Three corollaries are: (i) the $2
\to 4$ norm is NP-hard to approximate to precision
inverse-polynomial in the dimension, (ii) the $2 \to 4$
norm does not have a good approximation (in the sense
above) unless 3-SAT can be solved in time $\exp(\sqrt n
\poly \log (n))$, and (iii) known algorithms for the
quantum separability problem imply a non-trivial
additive approximation for the $2 \to 4$ norm.",
acknowledgement = ack-nhfb,
}
@InProceedings{Efremenko:2012:IRL,
author = "Klim Efremenko",
title = "From irreducible representations to locally decodable
codes",
crossref = "ACM:2012:SPA",
pages = "327--338",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214008",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A $q$-query Locally Decodable Code (LDC) is an
error-correcting code that allows to read any
particular symbol of the message by reading only $q$
symbols of the codeword even if the codeword is
adversary corrupted. In this paper we present a new
approach for the construction of LDCs. We show that if
there exists an irreducible representation $(\rho, V)$
of $G$ and $q$ elements $g_1$, $g_2$, \ldots{}, $g_q$
in $G$ such that there exists a linear combination of
matrices $\rho(g_i)$ that is of rank one, then we can
construct a $q$-query Locally Decodable Code $C: V \to
F^G$. We show the potential of this approach by
constructing constant query LDCs of sub-exponential
length matching the best known constructions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Guruswami:2012:FCF,
author = "Venkatesan Guruswami and Chaoping Xing",
title = "Folded codes from function field towers and improved
optimal rate list decoding",
crossref = "ACM:2012:SPA",
pages = "339--350",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214009",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give a new construction of algebraic codes which
are efficiently list decodable from a fraction $1 - R -
\epsilon$ of adversarial errors where $R$ is the rate
of the code, for any desired positive constant
$\epsilon$. The worst-case list size output by the
algorithm is $O(1 / \epsilon)$, matching the
existential bound for random codes up to constant
factors. Further, the alphabet size of the codes is a
constant depending only on $\epsilon$ --- it can be
made $\exp(\tilde{O}(1 / \epsilon^2))$ which is not
much worse than the non-constructive $\exp(1 /
\epsilon)$ bound of random codes. The code construction
is Monte Carlo and has the claimed list decoding
property with high probability. Once the code is
(efficiently) sampled, the encoding/decoding algorithms
are deterministic with a running time $O_{\epsilon}
(N^c)$ for an absolute constant $c$, where $N$ is the
code's block length. Our construction is based on a
careful combination of a linear-algebraic approach to
list decoding folded codes from towers of function
fields, with a special form of subspace-evasive sets.
Instantiating this with the explicit ``asymptotically
good'' Garcia--Stichtenoth (GS for short) tower of
function fields yields the above parameters. To
illustrate the method in a simpler setting, we also
present a construction based on Hermitian function
fields, which offers similar guarantees with a
list-size and alphabet size polylogarithmic in the
block length $N$. In comparison, algebraic codes
achieving the optimal trade-off between list
decodability and rate based on folded Reed--Solomon
codes have a decoding complexity of $N^{\Omega(1 /
\epsilon)}$, an alphabet size of $N^{\Omega(1 /
\epsilon 2)}$, and a list size of $O(1 / \epsilon^2)$
(even after combination with subspace-evasive sets).
Thus we get an improvement over the previous best
bounds in all three aspects simultaneously, and are
quite close to the existential random coding bounds.
Along the way, we shed light on how to use
automorphisms of certain function fields to enable list
decoding of the folded version of the associated
algebraic-geometric codes.",
acknowledgement = ack-nhfb,
}
@InProceedings{Dvir:2012:SES,
author = "Zeev Dvir and Shachar Lovett",
title = "Subspace evasive sets",
crossref = "ACM:2012:SPA",
pages = "351--358",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214010",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We construct explicit subspace-evasive sets. These are
subsets of $F^n$ of size $|F|^{(1- \epsilon)n}$ whose
intersection with any $k$-dimensional subspace is
bounded by a constant $c(k, \epsilon)$. This problem
was raised by Guruswami (CCC 2011) as it leads to
optimal rate list-decodable codes of constant list
size. The main technical ingredient is the construction
of $k$ low-degree polynomials whose common set of zeros
has small intersection with any $k$-dimensional
subspace.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kaufman:2012:ETR,
author = "Tali Kaufman and Alexander Lubotzky",
title = "Edge transitive {Ramanujan} graphs and symmetric
{LDPC} good codes",
crossref = "ACM:2012:SPA",
pages = "359--366",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214011",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present the first explicit construction of a binary
symmetric code with constant rate and constant distance
(i.e., good code). Moreover, the code is LDPC and its
constraint space is generated by the orbit of one
constant weight constraint under the group action. Our
construction provides the first symmetric LDPC good
codes. In particular, it solves the main open problem
raised by Kaufman and Wigderson {8}.",
acknowledgement = ack-nhfb,
}
@InProceedings{Makarychev:2012:AAS,
author = "Konstantin Makarychev and Yury Makarychev and
Aravindan Vijayaraghavan",
title = "Approximation algorithms for semi-random partitioning
problems",
crossref = "ACM:2012:SPA",
pages = "367--384",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214013",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In this paper, we propose and study a new semi-random
model for graph partitioning problems. We believe that
it captures many properties of real-world instances.
The model is more flexible than the semi-random model
of Feige and Kilian and planted random model of Bui,
Chaudhuri, Leighton and Sipser. We develop a general
framework for solving semi-random instances and apply
it to several problems of interest. We present constant
factor bi-criteria approximation algorithms for
semi-random instances of the Balanced Cut, Multicut,
Min Uncut, Sparsest Cut and Small Set Expansion
problems. We also show how to almost recover the
optimal solution if the instance satisfies an
additional expanding condition. Our algorithms work in
a wider range of parameters than most algorithms for
previously studied random and semi-random models.
Additionally, we study a new planted algebraic expander
model and develop constant factor bi-criteria
approximation algorithms for graph partitioning
problems in this model.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sharathkumar:2012:NLT,
author = "R. Sharathkumar and Pankaj K. Agarwal",
title = "A near-linear time $\epsilon$-approximation algorithm
for geometric bipartite matching",
crossref = "ACM:2012:SPA",
pages = "385--394",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214014",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "For point sets $A, B \subset \mathbb{R}^d$, $|A| = |B|
= n$, and for a parameter $\epsilon > 0$, we present an
algorithm that computes, in $O(n \poly(\log n, 1 /
\epsilon))$ time, an $\epsilon$-approximate perfect
matching of $A$ and $B$ with high probability; the
previously best known algorithm takes $\Omega(n^{3/2})$
time. We approximate the L$_p$-norm using a distance
function, $d(\cdot,\cdot)$ based on a randomly shifted
quad-tree. The algorithm iteratively generates an
approximate minimum-cost augmenting path under
$d(\cdot,\cdot)$ in time proportional to the length of
the path. We show that the total length of the
augmenting paths generated by the algorithm is $O((n /
\epsilon)\log n)$, implying that the running time of
our algorithm is $O(n \poly(\log n, 1 / \epsilon))$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Abraham:2012:UPD,
author = "Ittai Abraham and Ofer Neiman",
title = "Using petal-decompositions to build a low stretch
spanning tree",
crossref = "ACM:2012:SPA",
pages = "395--406",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214015",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove that any graph $G = (V, E)$ with $n$ points
and $m$ edges has a spanning tree $T$ such that
$\sum_{(u,v) \in E(G)} d_T(u,v) = O(m \log n \log \log
n)$. Moreover such a tree can be found in time $O(m
\log n \log \log n)$. Our result is obtained using a
new petal-decomposition approach which guarantees that
the radius of each cluster in the tree is at most $4$
times the radius of the induced subgraph of the cluster
in the original graph.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brunsch:2012:ISA,
author = "Tobias Brunsch and Heiko R{\"o}glin",
title = "Improved smoothed analysis of multiobjective
optimization",
crossref = "ACM:2012:SPA",
pages = "407--426",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214016",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present several new results about smoothed analysis
of multiobjective optimization problems. Motivated by
the discrepancy between worst-case analysis and
practical experience, this line of research has gained
a lot of attention in the last decade. We consider
problems in which $d$ linear and one arbitrary
objective function are to be optimized over a set $S
\subseteq \{0, 1\}^n$ of feasible solutions. We improve
the previously best known bound for the smoothed number
of Pareto-optimal solutions to $O(n^{2d} \phi^d)$,
where $\phi$ denotes the perturbation parameter.
Additionally, we show that for any constant $c$ the
$c$-th moment of the smoothed number of Pareto-optimal
solutions is bounded by $O((n^{2d} \phi^d)^c)$. This
improves the previously best known bounds
significantly. Furthermore, we address the criticism
that the perturbations in smoothed analysis destroy the
zero-structure of problems by showing that the smoothed
number of Pareto-optimal solutions remains polynomially
bounded even for zero-preserving perturbations. This
broadens the class of problems captured by smoothed
analysis and it has consequences for non-linear
objective functions. One corollary of our result is
that the smoothed number of Pareto-optimal solutions is
polynomially bounded for polynomial objective
functions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Leonardi:2012:PFA,
author = "Stefano Leonardi and Tim Roughgarden",
title = "Prior-free auctions with ordered bidders",
crossref = "ACM:2012:SPA",
pages = "427--434",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214018",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Prior-free auctions are robust auctions that assume no
distribution over bidders' valuations and provide
worst-case (input-by-input) approximation guarantees.
In contrast to previous work on this topic, we pursue
good prior-free auctions with non-identical bidders.
Prior-free auctions can approximate meaningful
benchmarks for non-identical bidders only when
``sufficient qualitative information'' about the bidder
asymmetry is publicly known. We consider digital goods
auctions where there is a total ordering of the bidders
that is known to the seller, where earlier bidders are
in some sense thought to have higher valuations. We use
the framework of Hartline and Roughgarden (STOC '08) to
define an appropriate revenue benchmark: the maximum
revenue that can be obtained from a bid vector using
prices that are nonincreasing in the bidder ordering
and bounded above by the second-highest bid. This
monotone-price benchmark is always as large as the
well-known fixed-price benchmark F$^{(2)}$, so
designing prior-free auctions with good approximation
guarantees is only harder. By design, an auction that
approximates the monotone-price benchmark satisfies a
very strong guarantee: it is, in particular,
simultaneously near-optimal for essentially every
Bayesian environment in which bidders' valuation
distributions have nonincreasing monopoly prices, or in
which the distribution of each bidder stochastically
dominates that of the next. Of course, even if there is
no distribution over bidders' valuations, such an
auction still provides a quantifiable input-by-input
performance guarantee. In this paper, we design a
simple prior-free auction for digital goods with
ordered bidders, the Random Price Restriction (RPR)
auction. We prove that its expected revenue on every
bid profile $b$ is $\Omega(M(b) / \log^*n)$, where $M$
denotes the monotone-price benchmark and $\log^*n$
denotes the number of times that the $\log_2$ operator
can be applied to $n$ before the result drops below a
fixed constant.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chawla:2012:LBB,
author = "Shuchi Chawla and Nicole Immorlica and Brendan
Lucier",
title = "On the limits of black-box reductions in mechanism
design",
crossref = "ACM:2012:SPA",
pages = "435--448",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214019",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider the problem of converting an arbitrary
approximation algorithm for a single-parameter
optimization problem into a computationally efficient
truthful mechanism. We ask for reductions that are
black-box, meaning that they require only oracle access
to the given algorithm and in particular do not require
explicit knowledge of the problem constraints. Such a
reduction is known to be possible, for example, for the
social welfare objective when the goal is to achieve
Bayesian truthfulness and preserve social welfare in
expectation. We show that a black-box reduction for the
social welfare objective is not possible if the
resulting mechanism is required to be truthful in
expectation and to preserve the worst-case
approximation ratio of the algorithm to within a
subpolynomial factor. Further, we prove that for other
objectives such as makespan, no black-box reduction is
possible even if we only require Bayesian truthfulness
and an average-case performance guarantee.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bei:2012:BFM,
author = "Xiaohui Bei and Ning Chen and Nick Gravin and Pinyan
Lu",
title = "Budget feasible mechanism design: from prior-free to
{Bayesian}",
crossref = "ACM:2012:SPA",
pages = "449--458",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214020",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Budget feasible mechanism design studies procurement
combinatorial auctions in which the sellers have
private costs to produce items, and the buyer
(auctioneer) aims to maximize a social valuation
function on subsets of items, under the budget
constraint on the total payment. One of the most
important questions in the field is ``which valuation
domains admit truthful budget feasible mechanisms with
'small' approximations (compared to the social
optimum)?'' Singer [35] showed that additive and
submodular functions have a constant approximation
mechanism. Recently, Dobzinski, Papadimitriou, and
Singer [20] gave an $O(\log^2 n)$ approximation
mechanism for subadditive functions; further, they
remarked that: ``A fundamental question is whether,
regardless of computational constraints, a
constant-factor budget feasible mechanism exists for
subadditive functions.'' In this paper, we address this
question from two viewpoints: prior-free worst case
analysis and Bayesian analysis, which are two standard
approaches from computer science and economics,
respectively. --- For the prior-free framework, we use
a linear program (LP) that describes the fractional
cover of the valuation function; the LP is also
connected to the concept of approximate core in
cooperative game theory. We provide a mechanism for
subadditive functions whose approximation is $O(I)$,
via the worst case integrality gap $I$ of this LP. This
implies an $O(\log n)$-approximation for subadditive
valuations, $O(1)$-approximation for XOS valuations, as
well as for valuations having a constant integrality
gap. XOS valuations are an important class of functions
and lie between the submodular and the subadditive
classes of valuations. We further give another
polynomial time $O(\log n / (\log \log n))$
sub-logarithmic approximation mechanism for subadditive
functions. Both of our mechanisms improve the best
known approximation ratio $O(\log^2 n)$. --- For the
Bayesian framework, we provide a constant approximation
mechanism for all subadditive functions, using the
above prior-free mechanism for XOS valuations as a
subroutine. Our mechanism allows correlations in the
distribution of private information and is universally
truthful.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cai:2012:ACM,
author = "Yang Cai and Constantinos Daskalakis and S. Matthew
Weinberg",
title = "An algorithmic characterization of multi-dimensional
mechanisms",
crossref = "ACM:2012:SPA",
pages = "459--478",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214021",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We show that every feasible, Bayesian, multi-item
multi-bidder mechanism for independent, additive
bidders can be implemented as a mechanism that: (a)
allocates every item independently of the other items;
(b) for the allocation of each item it uses a strict
ordering of all bidders' types; and allocates the item
using a distribution over hierarchical mechanisms that
iron this ordering into a non-strict ordering, and give
the item uniformly at random to the bidders whose
reported types dominate all other reported types
according to the non-strict ordering. Combined with
cyclic-monotonicity our results provide a
characterization of feasible, Bayesian Incentive
Compatible mechanisms in this setting. Our
characterization is enabled by a new, constructive
proof of Border's theorem [Border 1991], and a new
generalization of this theorem to independent (but not
necessarily identically distributed) bidders, improving
upon the results of [Border 2007, Che--Kim--Mierendorf
2011]. For a single item and independent bidders, we
show that every feasible reduced form auction can be
implemented as a distribution over hierarchical
mechanisms that are consistent with the same strict
ordering of all bidders' types, which every mechanism
in the support of the distribution irons to a
non-strict ordering. We also give a polynomial-time
algorithm for determining feasibility of a reduced form
auction, or providing a separation hyperplane from the
set of feasible reduced forms. To complete the picture,
we provide polynomial-time algorithms to find and
exactly sample from a distribution over hierarchical
mechanisms consistent with a given feasible reduced
form. All these results generalize to multi-item
reduced form auctions for independent, additive
bidders. Finally, for multiple items, additive bidders
with hard demand constraints, and arbitrary value
correlation across items or bidders, we give a proper
generalization of Border's Theorem, and characterize
feasible reduced form auctions as multi-commodity flows
in related multi-commodity flow instances. We also show
that our generalization holds for a broader class of
feasibility constraints, including the intersection of
any two matroids. As a corollary of our results we
compute revenue-optimal, Bayesian Incentive Compatible
(BIC) mechanisms in multi-item multi-bidder settings,
when each bidder has arbitrarily correlated values over
the items and additive valuations over bundles of
items, and the bidders are independent. Our mechanisms
run in time polynomial in the total number of bidder
types (and {not} type profiles). This running time is
polynomial in the number of bidders, but potentially
exponential in the number of items. We improve the
running time to polynomial in both the number of items
and the number of bidders by using recent structural
results on optimal BIC auctions in item-symmetric
settings [Daskalakis--Weinberg 2011].",
acknowledgement = ack-nhfb,
}
@InProceedings{Gal:2012:TBC,
author = "Anna G{\'a}l and Kristoffer Arnsfelt Hansen and Michal
Kouck{\'y} and Pavel Pudl{\'a}k and Emanuele Viola",
title = "Tight bounds on computing error-correcting codes by
bounded-depth circuits with arbitrary gates",
crossref = "ACM:2012:SPA",
pages = "479--494",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214023",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We bound the minimum number $w$ of wires needed to
compute any (asymptotically good) error-correcting code
$C: \{0, 1\}^{\Omega(n)} \to \{0, 1\}^n$ with minimum
distance $\Omega(n)$, using unbounded fan-in circuits
of depth $d$ with arbitrary gates. Our main results
are: (1) If $d = 2$ then $w = \Theta(n({\log n/ \log
\log n})^2)$. (2) If $d = 3$ then $w = \Theta(n \lg \lg
n)$. (3) If $d = 2k$ or $d = 2k + 1$ for some integer
$k \geq 2$ then $w = \Theta(n \lambda_k (n))$, where
$\lambda_1(n) = \lceil \log n \rceil$, $\lambda_{i +
1}(n) = \lambda_i*(n)$, and the $*$ operation gives how
many times one has to iterate the function $\lambda_i$
to reach a value at most $1$ from the argument $n$. (4)
If $d = \log * n$ then $w = O(n)$. For depth $d = 2$,
our $\Omega(n (\log n/\log \log n)^2)$ lower bound
gives the largest known lower bound for computing any
linear map. Using a result by Ishai, Kushilevitz,
Ostrovsky, and Sahai (2008), we also obtain similar
bounds for computing pairwise-independent hash
functions. Our lower bounds are based on a
superconcentrator-like condition that the graphs of
circuits computing good codes must satisfy. This
condition is provably intermediate between
superconcentrators and their weakenings considered
before.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chan:2012:TBM,
author = "Siu Man Chan and Aaron Potechin",
title = "Tight bounds for monotone switching networks via
{Fourier} analysis",
crossref = "ACM:2012:SPA",
pages = "495--504",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214024",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove tight size bounds on monotone switching
networks for the $k$-clique problem, and for an
explicit monotone problem by analyzing the generation
problem with a pyramid structure of height $h$. This
gives alternative proofs of the separations of $m$-NC
from $m$-P and of $m$-NC$^i$ from $m$-NC$^{i + 1}$,
different from Raz--McKenzie (Combinatorica '99). The
enumerative-combinatorial and Fourier analytic
techniques in this work are very different from a large
body of work on circuit depth lower bounds, and may be
of independent interest.",
acknowledgement = ack-nhfb,
}
@InProceedings{Braverman:2012:IIC,
author = "Mark Braverman",
title = "Interactive information complexity",
crossref = "ACM:2012:SPA",
pages = "505--524",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214025",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The primary goal of this paper is to define and study
the interactive information complexity of functions.
Let $f(x,y)$ be a function, and suppose Alice is given
$x$ and Bob is given $y$. Informally, the interactive
information complexity ${\rm IC}(f)$ of $f$ is the
least amount of information Alice and Bob need to
reveal to each other to compute $f$. Previously,
information complexity has been defined with respect to
a prior distribution on the input pairs $(x,y)$. Our
first goal is to give a definition that is independent
of the prior distribution. We show that several
possible definitions are essentially equivalent. We
establish some basic properties of the interactive
information complexity ${\rm IC}(f)$. In particular, we
show that ${\rm IC}(f)$ is equal to the amortized
(randomized) communication complexity of $f$. We also
show a direct sum theorem for ${\rm IC}(f)$ and give
the first general connection between information
complexity and (non-amortized) communication
complexity. This connection implies that a non-trivial
exchange of information is required when solving
problems that have non-trivial communication
complexity. We explore the information complexity of
two specific problems --- Equality and Disjointness. We
show that only a constant amount of information needs
to be exchanged when solving Equality with no errors,
while solving Disjointness with a constant error
probability requires the parties to reveal a linear
amount of information to each other.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sherstov:2012:MCC,
author = "Alexander A. Sherstov",
title = "The multiparty communication complexity of set
disjointness",
crossref = "ACM:2012:SPA",
pages = "525--548",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214026",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the set disjointness problem in the
number-on-the-forehead model of multiparty
communication.\par
(i) We prove that $k$-party set disjointness has
communication complexity $\Omega(n/4^k)^{1/4}$ in the
randomized and nondeterministic models and
$\Omega(n/4^k)^{1/8}$ in the Merlin--Arthur model.
These lower bounds are close to tight. Previous lower
bounds (2007-2008) for $k \geq 3$ parties were weaker
than $\Omega(n/2^{k^3})^{1 / (k + 1)}$ in all three
models.\par
(ii) We prove that solving $\ell$ instances of set
disjointness requires $\ell \cdot \Omega(n/4^k)^{1/4}$
bits of communication, even to achieve correctness
probability exponentially close to $1/2$. This gives
the first direct-product result for multiparty set
disjointness, solving an open problem due to Beame,
Pitassi, Segerlind, and Wigderson (2005).\par
(iii) We construct a read-once $\{\wedge,
\vee\}$-circuit of depth 3 with exponentially small
discrepancy for up to $k \approx (1/2)\log n$ parties.
This result is optimal with respect to depth and solves
an open problem due to Beame and Huynh-Ngoc (FOCS '09),
who gave a depth-$6$ construction. Applications to
circuit complexity are given.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cheung:2012:FMR,
author = "Ho Yee Cheung and Tsz Chiu Kwok and Lap Chi Lau",
title = "Fast matrix rank algorithms and applications",
crossref = "ACM:2012:SPA",
pages = "549--562",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214028",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider the problem of computing the rank of an $m
\times n$ matrix $A$ over a field. We present a
randomized algorithm to find a set of $r = \rank(A)$
linearly independent columns in $O(|A| + r^w)$ field
operations, where $|A|$ denotes the number of nonzero
entries in $A$ and $w < 2.38$ is the matrix
multiplication exponent. Previously the best known
algorithm to find a set of $r$ linearly independent
columns is by Gaussian elimination, with running time
$O(m n r^w)$. Our algorithm is faster when $r <
\max\{m, n\}$, for instance when the matrix is
rectangular. We also consider the problem of computing
the rank of a matrix dynamically, supporting the
operations of rank one updates and additions and
deletions of rows and columns. We present an algorithm
that updates the rank in $O(m n)$ field operations. We
show that these algorithms can be used to obtain faster
algorithms for various problems in numerical linear
algebra, combinatorial optimization and dynamic data
structure.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hassanieh:2012:NOS,
author = "Haitham Hassanieh and Piotr Indyk and Dina Katabi and
Eric Price",
title = "Nearly optimal sparse {Fourier} transform",
crossref = "ACM:2012:SPA",
pages = "563--578",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214029",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider the problem of computing the $k$-sparse
approximation to the discrete Fourier transform of an
$n$-dimensional signal. We show:\par
(1) An $O(k \log n)$-time randomized algorithm for the
case where the input signal has at most $k$ non-zero
Fourier coefficients, and\par
(2) An $O(k \log n \log (n/k))$-time randomized
algorithm for general input signals.\par
Both algorithms achieve $o(n \log n)$ time, and thus
improve over the Fast Fourier Transform, for any $k =
o(n)$. They are the first known algorithms that satisfy
this property. Also, if one assumes that the Fast
Fourier Transform is optimal, the algorithm for the
exactly $k$-sparse case is optimal for any $k =
n^{\Omega(1)}$.\par
We complement our algorithmic results by showing that
any algorithm for computing the sparse Fourier
transform of a general signal must use at least
$\Omega(k \log (n / k) / \log \log n)$ signal samples,
even if it is allowed to perform adaptive sampling.",
acknowledgement = ack-nhfb,
}
@InProceedings{Etessami:2012:PTA,
author = "Kousha Etessami and Alistair Stewart and Mihalis
Yannakakis",
title = "Polynomial time algorithms for multi-type branching
processes and stochastic context-free grammars",
crossref = "ACM:2012:SPA",
pages = "579--588",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214030",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We show that one can approximate the least fixed point
solution for a multivariate system of monotone
probabilistic polynomial equations in time polynomial
in both the encoding size of the system of equations
and in $\log (1 / \epsilon)$, where $\epsilon > 0$ is
the desired additive error bound of the solution. (The
model of computation is the standard Turing machine
model.) We use this result to resolve several open
problems regarding the computational complexity of
computing key quantities associated with some classic
and heavily studied stochastic processes, including
multi-type branching processes and stochastic
context-free grammars.",
acknowledgement = ack-nhfb,
}
@InProceedings{Adamaszek:2012:OOB,
author = "Anna Adamaszek and Artur Czumaj and Matthias Englert
and Harald R{\"a}cke",
title = "Optimal online buffer scheduling for block devices",
crossref = "ACM:2012:SPA",
pages = "589--598",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214031",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We introduce a buffer scheduling problem for block
operation devices in an online setting. We consider a
stream of items of different types to be processed by a
block device. The block device can process all items of
the same type in a single step. To improve the
performance of the system a buffer of size $k$ is used
to store items in order to reduce the number of
operations required. Whenever the buffer becomes full a
buffer scheduling strategy has to select one type and
then a block operation on all elements with this type
that are currently in the buffer is performed. The goal
is to design a scheduling strategy that minimizes the
number of block operations required. In this paper we
consider the online version of this problem, where the
buffer scheduling strategy must make decisions without
knowing the future items that appear in the input
stream. Our main result is the design of an $O(\log
\log k)$-competitive online randomized buffer
scheduling strategy. The bound is asymptotically tight.
As a byproduct of our LP-based techniques, we obtain a
randomized offline algorithm that approximates the
optimal number of block operations to within a constant
factor.",
acknowledgement = ack-nhfb,
}
@InProceedings{Agrawal:2012:JHC,
author = "Manindra Agrawal and Chandan Saha and Ramprasad
Saptharishi and Nitin Saxena",
title = "{Jacobian} hits circuits: hitting-sets, lower bounds
for depth-{D} occur-$k$ formulas \& depth-$3$
transcendence degree-$k$ circuits",
crossref = "ACM:2012:SPA",
pages = "599--614",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214033",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present a single common tool to strictly subsume
all known cases of polynomial time blackbox polynomial
identity testing (PIT), that have been hitherto solved
using diverse tools and techniques, over fields of zero
or large characteristic. In particular, we show that
polynomial time hitting-set generators for identity
testing of the two seemingly different and well studied
models --- depth-3 circuits with bounded top fanin, and
constant-depth constant-read multilinear formulas ---
can be constructed using one common algebraic-geometry
theme: Jacobian captures algebraic independence. By
exploiting the Jacobian, we design the first efficient
hitting-set generators for broad generalizations of the
above-mentioned models, namely:\par
(1) depth-3 $(\Omega \Pi \Omega)$ circuits with
constant transcendence degree of the polynomials
computed by the product gates (no bounded top fanin
restriction), and\par
(2) constant-depth constant-{\em occur\/} formulas (no
multilinear restriction).\par
Constant-{\rm occur} of a variable, as we define it, is
a much more general concept than constant-read. Also,
earlier work on the latter model assumed that the
formula is multilinear. Thus, our work goes further
beyond the related results obtained by Saxena \&
Seshadhri (STOC 2011), Saraf \& Volkovich (STOC 2011),
Anderson et al. (CCC 2011), Beecken et al. (ICALP 2011)
and Grenet et al. (FSTTCS 2011), and brings them under
one unifying technique.\par
In addition, using the same Jacobian based approach, we
prove exponential lower bounds for the immanant (which
includes permanent and determinant) on the same
depth-$3$ and depth-$4$ models for which we give
efficient PIT algorithms. Our results reinforce the
intimate connection between identity testing and lower
bounds by exhibiting a concrete mathematical tool ---
the Jacobian --- that is equally effective in solving
both the problems on certain interesting and previously
well-investigated (but not well understood) models of
computation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Dvir:2012:SMB,
author = "Zeev Dvir and Guillaume Malod and Sylvain Perifel and
Amir Yehudayoff",
title = "Separating multilinear branching programs and
formulas",
crossref = "ACM:2012:SPA",
pages = "615--624",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214034",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "This work deals with the power of linear algebra in
the context of multilinear computation. By linear
algebra we mean algebraic branching programs (ABPs)
which are known to be computationally equivalent to two
basic tools in linear algebra: iterated matrix
multiplication and the determinant. We compare the
computational power of multilinear ABPs to that of
multilinear arithmetic formulas, and prove a tight
super-polynomial separation between the two models.
Specifically, we describe an explicit $n$-variate
polynomial $F$ that is computed by a linear-size
multilinear ABP but every multilinear formula computing
$F$ must be of size n$^{ \Omega(\log n)}$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Gupta:2012:RDM,
author = "Ankit Gupta and Neeraj Kayal and Satya Lokam",
title = "Reconstruction of depth-$4$ multilinear circuits with
top fan-in $2$",
crossref = "ACM:2012:SPA",
pages = "625--642",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214035",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present a randomized algorithm for reconstructing
multilinear $\Sigma \Pi \Sigma \Pi (2)$ circuits, i.e.,
multilinear depth-$4$ circuits with fan-in $2$ at the
top $+$ gate. The algorithm is given blackbox access to
a polynomial $f \in F[x_1,\ldots{},x_n]$ computable by
a multilinear $\Sigma \Pi \Sigma \Pi (2)$ circuit of
size $s$ and outputs an equivalent multilinear $\Sigma
\Pi \Sigma \Pi (2)$ circuit, runs in time $\poly(n,s)$,
and works over any field $F$. This is the first
reconstruction result for any model of depth-$4$
arithmetic circuits. Prior to our work, reconstruction
results for bounded depth circuits were known only for
depth-$2$ arithmetic circuits (Klivans \& Spielman,
STOC 2001), $\Sigma \Pi \Sigma (2)$ circuits (depth-$3$
arithmetic circuits with top fan-in $2$) (Shpilka, STOC
2007), and $\Sigma \Pi \Sigma (k)$ with $k = O(1)$
(Karnin \& Shpilka, CCC 2009). Moreover, the running
times of these algorithms have a polynomial dependence
on $4|F|$ and hence do not work for infinite fields
such as $Q$. Our techniques are quite different from
the previous ones for depth-$3$ reconstruction and rely
on a polynomial operator introduced by Karnin et al.
(STOC 2010) and Saraf \& Volkovich (STOC 2011) for
devising blackbox identity tests for multilinear
$\Sigma \Pi \Sigma \Pi (k)$ circuits. Some other
ingredients of our algorithm include the classical
multivariate blackbox factoring algorithm by Kaltofen
\& Trager (FOCS 1988) and an average-case algorithm for
reconstructing $\Sigma \Pi \Sigma (2)$ circuits by
Kayal.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kayal:2012:APP,
author = "Neeraj Kayal",
title = "Affine projections of polynomials: extended abstract",
crossref = "ACM:2012:SPA",
pages = "643--662",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214036",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "An $m$-variate polynomial $f$ is said to be an affine
projection of some $n$-variate polynomial $g$ if there
exists an $n m$ matrix $A$ and an $n$-dimensional
vector $b$ such that $f(x) = g(Ax + b)$. In other
words, if $f$ can be obtained by replacing each
variable of $g$ by an affine combination of the
variables occurring in $f$, then it is said to be an
affine projection of $g$. Some well known problems
(such as the determinant versus permanent and matrix
multiplication for example) are instances of this
problem. Given $f$ and $g$ can we determine whether $f$
is an affine projection of $g$? The intention of this
paper is to understand the complexity of the
corresponding computational problem: given polynomials
$f$ and $g$ find $A$ and $b$ such that $f = g(A x +
b)$, if such an $(A b)$ exists. We first show that this
is an NP-hard problem. We then focus our attention on
instances where $g$ is a member of some fixed, well
known family of polynomials so that the input consists
only of the polynomial $f(x)$ having $m$ variables and
degree $d$. We consider the situation where $f(x)$ is
given to us as a blackbox (i.e. for any point $aFm$ we
can query the blackbox and obtain $f(a)$ in one step)
and devise randomized algorithms with running time
$\poly(m n d)$ in the following special cases. Firstly
where $g$ is the Permanent (respectively the
Determinant) of an $n \times n$ matrix and $A$ is of
rank $n^2$. Secondly where $g$ is the sum of powers
polynomial (respectively the sum of products
polynomial), and $A$ is a random matrix of the
appropriate dimensions (also $d$ should not be too
small).",
acknowledgement = ack-nhfb,
}
@InProceedings{Bartal:2012:TSP,
author = "Yair Bartal and Lee-Ad Gottlieb and Robert
Krauthgamer",
title = "The traveling salesman problem: low-dimensionality
implies a polynomial time approximation scheme",
crossref = "ACM:2012:SPA",
pages = "663--672",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214038",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The Traveling Salesman Problem (TSP) is among the most
famous NP-hard optimization problems. We design for
this problem a randomized polynomial-time algorithm
that computes a $(1 + \mu)$-approximation to the
optimal tour, for any fixed $\mu > 0$, in TSP instances
that form an arbitrary metric space with bounded
intrinsic dimension. The celebrated results of Arora
[Aro98] and Mitchell [Mit99] prove that the above
result holds in the special case of TSP in a
fixed-dimensional Euclidean space. Thus, our algorithm
demonstrates that the algorithmic tractability of
metric TSP depends on the dimensionality of the space
and not on its specific geometry. This result resolves
a problem that has been open since the quasi-polynomial
time algorithm of Talwar [Tal04].",
acknowledgement = ack-nhfb,
}
@InProceedings{Chuzhoy:2012:VSS,
author = "Julia Chuzhoy",
title = "On vertex sparsifiers with {Steiner} nodes",
crossref = "ACM:2012:SPA",
pages = "673--688",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214039",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Given an undirected graph $G = (V, E)$ with edge
capacities $c_e \geq 1$ for $e \in E$ and a subset $T$
of $k$ vertices called terminals, we say that a graph
$H$ is a quality-$q$ cut sparsifier for $G$ iff $T
\subseteq V(H)$, and for any partition $(A, B)$ of $T$,
the values of the minimum cuts separating $A$ and $B$
in graphs $G$ and $H$ are within a factor $q$ from each
other. We say that $H$ is a quality-$q$ flow sparsifier
for $G$ iff $T \subseteq V(H)$, and for any set $D$ of
demands over the terminals, the values of the minimum
edge congestion incurred by fractionally routing the
demands in $D$ in graphs $G$ and $H$ are within a
factor $q$ from each other.\par
So far vertex sparsifiers have been studied in a
restricted setting where the sparsifier $H$ is not
allowed to contain any non-terminal vertices, that is
$V(H) = {\cal T}$. For this setting, efficient
algorithms are known for constructing quality-$O(\log
k/\log \log k)$ cut and flow vertex sparsifiers, as
well as a lower bound of $\tilde{\Omega}(\sqrt{\log
k})$ on the quality of any flow or cut
sparsifier.\par
We study flow and cut sparsifiers in the more general
setting where Steiner vertices are allowed, that is, we
no longer require that $V(H) = {\cal T}$. We show
algorithms to construct constant-quality cut
sparsifiers of size $O(C^3)$ in time $\poly(n) \cdot
2^C$, and constant-quality flow sparsifiers of size
$C^{O(\log \log C)}$ in time $n^{O(\log C)} \cdot 2^C$,
where $C$ is the total capacity of the edges incident
on the terminals.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chalermsook:2012:AAH,
author = "Parinya Chalermsook and Julia Chuzhoy and Alina Ene
and Shi Li",
title = "Approximation algorithms and hardness of integral
concurrent flow",
crossref = "ACM:2012:SPA",
pages = "689--708",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214040",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study an integral counterpart of the classical
Maximum Concurrent Flow problem, that we call Integral
Concurrent Flow (ICF). In the basic version of this
problem (basic-ICF), we are given an undirected
$n$-vertex graph $G$ with edge capacities $c(e)$, a
subset $T$ of vertices called terminals, and a demand
$D(t,t')$ for every pair $(t,t')$ of the terminals. The
goal is to find a maximum value $\lambda$, and a
collection $P$ of paths, such that every pair $(t,t')$
of terminals is connected by $\lfloor \lambda \cdot
D(t,t') \rfloor$ paths in $P$, and the number of paths
containing any edge $e$ is at most $c(e)$. We show an
algorithm that achieves a $\poly \log n$-approximation
for basic-ICF, while violating the edge capacities by
only a constant factor. We complement this result by
proving that no efficient algorithm can achieve a
factor $\alpha$-approximation with congestion $c$ for
any values $\alpha$, $c$ satisfying $\alpha \cdot c =
O(\log \log n / \log \log \log n)$, unless NP
$\subseteq$ ZPTIME(n$^{\poly \log n}$). We then turn to
study the more general group version of the problem
(group = ICF), in which we are given a collection
$(S_1, T_1), \ldots{}, (S_k, T_k)$ of pairs of vertex
subsets, and for each $1 \leq $i$ \leq k$, a demand
D$_i$ is specified. The goal is to find a maximum value
$\lambda$ and a collection $P$ of paths, such that for
each $i$, at least $\lfloor \lambda \cdot D_i \rfloor$
paths connect the vertices of $S_i$ to the vertices of
$T_i$, while respecting the edge capacities. We show
that for any $1 \leq $c$ \leq O(\log \log n)$, no
efficient algorithm can achieve a factor $O(n^{1/(2 2c
+ 3)})$-approximation with congestion $c$ for the
problem, unless NP $\subseteq$ DTIME($n^{O(\log \log
n)}$). On the other hand, we show an efficient
randomized algorithm that finds a $\poly \log
n$-approximate solution with a constant congestion, if
we are guaranteed that the optimal solution contains at
least $D \geq $k$ \poly \log n$ paths connecting every
pair (S$_i$, T$_i$).",
acknowledgement = ack-nhfb,
}
@InProceedings{Daskalakis:2012:LPB,
author = "Constantinos Daskalakis and Ilias Diakonikolas and
Rocco A. Servedio",
title = "Learning {Poisson} binomial distributions",
crossref = "ACM:2012:SPA",
pages = "709--728",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214042",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider a basic problem in unsupervised learning:
learning an unknown Poisson Binomial Distribution. A
Poisson Binomial Distribution (PBD) over $\{0,
1,\ldots{}, n\}$ is the distribution of a sum of $n$
independent Bernoulli random variables which may have
arbitrary, potentially non-equal, expectations. These
distributions were first studied by S. Poisson in 1837
and are a natural $n$-parameter generalization of the
familiar Binomial Distribution. Surprisingly, prior to
our work this basic learning problem was poorly
understood, and known results for it were far from
optimal. We essentially settle the complexity of the
learning problem for this basic class of distributions.
As our main result we give a highly efficient algorithm
which learns to $\epsilon$-accuracy using $O(1 /
\epsilon^3)$ samples independent of $n$. The running
time of the algorithm is quasilinear in the size of its
input data, i.e. $\tilde{O}(\log (n)/ \epsilon^3)$
bit-operations (observe that each draw from the
distribution is a $\log(n)$-bit string). This is nearly
optimal since any algorithm must use $\Omega(1 /
\epsilon^2)$ samples. We also give positive and
negative results for some extensions of this learning
problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{De:2012:NOS,
author = "Anindya De and Ilias Diakonikolas and Vitaly Feldman
and Rocco A. Servedio",
title = "Nearly optimal solutions for the chow parameters
problem and low-weight approximation of halfspaces",
crossref = "ACM:2012:SPA",
pages = "729--746",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214043",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The Chow parameters of a Boolean function $f: \{-1,
1\}^n \to \{-1, 1\}$ are its $n + 1$ degree-$0$ and
degree-$1$ Fourier coefficients. It has been known
since 1961 [Cho61, Tan61] that the (exact values of
the) Chow parameters of any linear threshold function
$f$ uniquely specify $f$ within the space of all
Boolean functions, but until recently [OS11] nothing
was known about efficient algorithms for reconstructing
$f$ (exactly or approximately) from exact or
approximate values of its Chow parameters. We refer to
this reconstruction problem as the Chow Parameters
Problem. Our main result is a new algorithm for the
Chow Parameters Problem which, given (sufficiently
accurate approximations to) the Chow parameters of any
linear threshold function f, runs in time
$\tilde{O}(n^2) o(1/ \epsilon)^{O(\log 2 (1 /
\epsilon))}$ and with high probability outputs a
representation of an LTF $f'$ that is $\epsilon$-close
to $f$. The only previous algorithm [OS11] had running
time $\poly(n) \cdot 2^{2 \tilde{O}(1 / \epsilon 2)}$.
As a byproduct of our approach, we show that for any
linear threshold function $f$ over ${-1,1}^n$, there is
a linear threshold function $f'$ which is
$\epsilon$-close to $f$ and has all weights that are
integers at most $\sqrt n o(1 / \epsilon)^{O(\log 2 (1
/ \epsilon))}$. This significantly improves the best
previous result of [Serv09] which gave a $\poly(n) o
2^{O(1 / \epsilon 2/3)}$ weight bound, and is close to
the known lower bound of $\max\{\sqrt n, (1 /
\epsilon)^{\Omega(\log \log (1 / \epsilon))}\}$
[Gol06,Serv07]. Our techniques also yield improved
algorithms for related problems in learning theory. In
addition to being significantly stronger than previous
work, our results are obtained using conceptually
simpler proofs. The two main ingredients underlying our
results are (1) a new structural result showing that
for $f$ any linear threshold function and g any bounded
function, if the Chow parameters of $f$ are close to
the Chow parameters of $g$ then $f$ is close to g; (2)
a new boosting-like algorithm that given approximations
to the Chow parameters of a linear threshold function
outputs a bounded function whose Chow parameters are
close to those of $f$.",
}
@InProceedings{Sherstov:2012:MPR,
author = "Alexander A. Sherstov",
title = "Making polynomials robust to noise",
crossref = "ACM:2012:SPA",
pages = "747--758",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214044",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A basic question in any computational model is how to
reliably compute a given function when the inputs or
intermediate computations are subject to noise at a
constant rate. Ideally, one would like to use at most a
constant factor more resources compared to the
noise-free case. This question has been studied for
decision trees, circuits, automata, data structures,
broadcast networks, communication protocols, and other
models. Buhrman et al. (2003) posed the noisy
computation problem for real polynomials. We give a
complete solution to this problem. For any polynomial
$p : \{0, 1\}^n \to [-1, 1]$, we construct a polynomial
$p_{\rm robust}: R^n \to R$ of degree $O(\deg p +
\log(1 / \epsilon))$ that $\epsilon$-approximates $p$
and is robust to noise in the inputs: $|p(x) - p_{\rm
robust} (x + \delta)| < \epsilon$ for all $x \in \{0,
1\}^n$ and all $\delta \in [-1/3, 1/3]^n$. This result
is optimal with respect to all parameters. We construct
$p_{\rm robust}$ explicitly for each $p$. Previously,
it was open to give such a construction even for $p =
x_1 \oplus x_2 \oplus \ldots{} \oplus x_n$ (Buhrman et
al., 2003). The proof contributes a technique of
independent interest, which allows one to force partial
cancellation of error terms in a polynomial.",
acknowledgement = ack-nhfb,
}
@InProceedings{Goyal:2012:CCN,
author = "Sanjeev Goyal and Michael Kearns",
title = "Competitive contagion in networks",
crossref = "ACM:2012:SPA",
pages = "759--774",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214046",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We develop a game-theoretic framework for the study of
competition between firms who have budgets to ``seed''
the initial adoption of their products by consumers
located in a social network. The payoffs to the firms
are the eventual number of adoptions of their product
through a competitive stochastic diffusion process in
the network. This framework yields a rich class of
competitive strategies, which depend in subtle ways on
the stochastic dynamics of adoption, the relative
budgets of the players, and the underlying structure of
the social network. We identify a general property of
the adoption dynamics --- namely, decreasing returns to
local adoption --- for which the inefficiency of
resource use at equilibrium (the Price of Anarchy) is
uniformly bounded above, across all networks. We also
show that if this property is violated the Price of
Anarchy can be unbounded, thus yielding sharp threshold
behavior for a broad class of dynamics. We also
introduce a new notion, the Budget Multiplier, that
measures the extent that imbalances in player budgets
can be amplified at equilibrium. We again identify a
general property of the adoption dynamics --- namely,
proportional local adoption between competitors --- for
which the (pure strategy) Budget Multiplier is
uniformly bounded above, across all networks. We show
that a violation of this property can lead to unbounded
Budget Multiplier, again yielding sharp threshold
behavior for a broad class of dynamics.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cebrian:2012:FRB,
author = "Manuel Cebrian and Lorenzo Coviello and Andrea Vattani
and Panagiotis Voulgaris",
title = "Finding red balloons with split contracts: robustness
to individuals' selfishness",
crossref = "ACM:2012:SPA",
pages = "775--788",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214047",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The present work deals with the problem of information
acquisition in a strategic networked environment. To
study this problem, Kleinberg and Raghavan (FOCS 2005)
introduced the model of {\em query incentive networks},
where the root of a binomial branching process wishes
to retrieve an information --- known by each node
independently with probability 1/n --- by investing as
little as possible. The authors considered {\em
fixed-payment contracts\/} in which every node
strategically chooses an amount to offer its children
paid upon information retrieval to convince them to
seek the information in their subtrees. Kleinberg and
Raghavan discovered that the investment needed at the
root exhibits an unexpected threshold behavior that
depends on the branching parameter b. For b > 2, the
investment is linear in the expected distance to the
closest information (logarithmic in $n$, the rarity of
the information), while, for $1 < b < 2$, it becomes
exponential in the same distance (i.e., polynomial in
$n$). Arcaute et al. (EC 2007) later observed the same
threshold behavior for arbitrary Galton--Watson
branching processes.\par
The DARPA Network Challenge --- retrieving the
locations of ten balloons placed at undisclosed
positions in the US --- has recently brought practical
attention to the problems of social mobilization and
information acquisition in a networked environment. The
MIT Media Laboratory team won the challenge by acting
as the root of a query incentive network that unfolded
all over the world. However, rather than adopting a
{\em fixed-payment strategy}, the team implemented a
different incentive scheme based on {\em $1/2$-split
contracts}. Under such incentive scheme, a node $u$ who
does not possess the information can recruit a friend
$v$ through a contract stipulating that if the
information is found in the subtree rooted at $v$, then
$v$ has to give half of her own reward back to
$u$.\par
Motivated by its empirical success, we present a
comprehensive theoretical study of this scheme in the
game theoretical setting of query incentive networks.
Our main result is that split contracts are robust ---
as opposed to fixed-payment contracts --- to nodes'
selfishness. Surprisingly, when nodes determine the
splits to offer their children based on the contracts
received from their recruiters, the threshold behavior
observed in the previous work vanishes, and an
investment linear in the expected distance to the
closest information is sufficient to retrieve the
information in {\em any arbitrary\/} Galton--Watson
process with $b > 1$. Finally, while previous analyses
considered the parameters of the branching process as
constants, we are able to characterize the rate of the
investment in terms of the branching process and the
desired probability of success. This allows us to show
improvements even in other special cases.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brandt:2012:AOD,
author = "Christina Brandt and Nicole Immorlica and Gautam
Kamath and Robert Kleinberg",
title = "An analysis of one-dimensional {Schelling}
segregation",
crossref = "ACM:2012:SPA",
pages = "789--804",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214048",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We analyze the Schelling model of segregation in which
a society of $n$ individuals live in a ring. Each
individual is one of two races and is only satisfied
with his location so long as at least half his 2w
nearest neighbors are of the same race as him. In the
dynamics, randomly-chosen unhappy individuals
successively swap locations. We consider the average
size of monochromatic neighborhoods in the final stable
state. Our analysis is the first rigorous analysis of
the Schelling dynamics. We note that, in contrast to
prior approximate analyses, the final state is nearly
integrated: the average size of monochromatic
neighborhoods is independent of $n$ and polynomial in
w.",
acknowledgement = ack-nhfb,
}
@InProceedings{Applebaum:2012:PGL,
author = "Benny Applebaum",
title = "Pseudorandom generators with long stretch and low
locality from random local one-way functions",
crossref = "ACM:2012:SPA",
pages = "805--816",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214050",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We continue the study of {\em locally-computable\/}
pseudorandom generators (PRG) $G : \{0, 1\}^n \to \{0,
1\}^m$ that each of their outputs depend on a small
number of $d$ input bits. While it is known that such
generators are likely to exist for the case of small
sub-linear stretch $m = n + n^{1 - \delta}$, it is less
clear whether achieving larger stretch such as $m = n +
\Omega(n)$, or even $m = n^{1 + \delta}$ is possible.
The existence of such PRGs, which was posed as an open
question in previous works, has recently gained an
additional motivation due to several interesting
applications.\par
We make progress towards resolving this question by
obtaining several local constructions based on the
one-wayness of ``random'' local functions --- a variant
of an assumption made by Goldreich (ECCC 2000).
Specifically, we construct collections of PRGs with the
following parameters:\par
1. Linear stretch $m = n + \Omega(n)$ and constant
locality $d = O(1)$.\par
2. Polynomial stretch $m = n^{1 + \delta}$ and {\em
any\/} (arbitrarily slowly growing) super-constant
locality $d = \omega(1)$, e.g., $\log^*n$.\par
3. Polynomial stretch $m = n^{1 + \delta}$, constant
locality $d = O(1)$, and inverse polynomial
distinguishing advantage (as opposed to the standard
case of $n^{-\omega(1)}$).\par
As an additional contribution, we show that our
constructions give rise to strong inapproximability
results for the densest-subgraph problem in $d$-uniform
hypergraphs for constant $d$. This allows us to improve
the previous bounds of Feige (STOC 2002) and Khot (FOCS
2004) from constant inapproximability factor to
$n^\epsilon$-inapproximability, at the expense of
relying on stronger assumptions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Vadhan:2012:CPS,
author = "Salil Vadhan and Colin Jia Zheng",
title = "Characterizing pseudoentropy and simplifying
pseudorandom generator constructions",
crossref = "ACM:2012:SPA",
pages = "817--836",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214051",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We provide a characterization of pseudoentropy in
terms of hardness of sampling: Let $(X, B)$ be jointly
distributed random variables such that $B$ takes values
in a polynomial-sized set. We show that $B$ is
computationally indistinguishable from a random
variable of higher Shannon entropy given $X$ if and
only if there is no probabilistic polynomial-time $S$
such that $(X, S(X))$ has small KL divergence from $(X,
B)$. This can be viewed as an analogue of the
Impagliazzo Hardcore Theorem (FOCS '95) for Shannon
entropy (rather than min-entropy).\par
Using this characterization, we show that if $f$ is a
one-way function, then $(f(U_n), U_n)$ has ``next-bit
pseudoentropy'' at least $n + \log n$, establishing a
conjecture of Haitner, Reingold, and Vadhan (STOC '10).
Plugging this into the construction of Haitner et al.,
this yields a simpler construction of pseudorandom
generators from one-way functions. In particular, the
construction only performs hashing once, and only needs
the hash functions that are randomness extractors (e.g.
universal hash functions) rather than needing them to
support ``local list-decoding'' (as in the
Goldreich--Levin hardcore predicate, STOC
'89).\par
With an additional idea, we also show how to improve
the seed length of the pseudorandom generator to
$\tilde{O}(n^3)$, compared to $\tilde{O}(n^4)$ in the
construction of Haitner et al.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2012:DEN,
author = "Xin Li",
title = "Design extractors, non-malleable condensers and
privacy amplification",
crossref = "ACM:2012:SPA",
pages = "837--854",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214052",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We introduce a new combinatorial object, called a
design extractor, that has both the properties of a
design and an extractor. We give efficient
constructions of such objects and show that they can be
used in several applications.\par
1. {\bf Improving the output length of known
non-malleable extractors.} Non-malleable extractors
were introduced in [DW09] to study the problem of
privacy amplification with an active adversary.
Currently, only two explicit constructions are known
[DLWZ11, CRS11]. Both constructions work for $n$ bit
sources with min-entropy $k > n / 2$. However, in both
constructions the output length is smaller than the
seed length, while the probabilistic method shows that
to achieve error $\epsilon$, one can use $O(\log n +
\log (1 / \epsilon))$ bits to extract up to $k/2$
output bits. In this paper, we use our design extractor
to give an explicit non-malleable extractor for
min-entropy $k > n / 2$, that has seed length $O(\log n
+ \log (1 / \epsilon))$ and output length
$\Omega(k)$.\par
2. {\bf Non-malleable condensers.} We introduce and
define the notion of a {\em non-malleable condenser}. A
non-malleable condenser is a generalization and
relaxation of a non-malleable extractor. We show that
similar as extractors and condensers, non-malleable
condensers can be used to construct non-malleable
extractors. We then show that our design extractor
already gives a non-malleable condenser for min-entropy
$k > n / 2$, with error $\epsilon$ and seed length
$O(\log (1 / \epsilon))$.\par
3. {\bf A new optimal protocol for privacy
amplification.} More surprisingly, we show that
non-malleable condensers themselves give optimal
privacy amplification protocols with an active
adversary. In fact, the non-malleable condensers used
in these protocols are much weaker compared to
non-malleable extractors, in the sense that the entropy
rate of the condenser's output does not need to
increase at all. This suggests that one promising next
step to achieve better privacy amplification protocols
may be to construct non-malleable condensers for
smaller min-entropy. As a by-product, we also obtain a
new explicit $2$-round privacy amplification protocol
with optimal entropy loss and optimal communication
complexity for min-entropy $k > n / 2$, without using
non-malleable extractors.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chuzhoy:2012:RUG,
author = "Julia Chuzhoy",
title = "Routing in undirected graphs with constant
congestion",
crossref = "ACM:2012:SPA",
pages = "855--874",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214054",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Given an undirected graph $G = (V,E)$, a collection
$(s_1, t_1)$, \ldots{}, $(s_k, t_k)$ of $k$ demand
pairs, and an integer $c$, the goal in the Edge
Disjoint Paths with Congestion problem is to connect
maximum possible number of the demand pairs by paths,
so that the maximum load on any edge (called edge
congestion) does not exceed $c$. We show an efficient
randomized algorithm that routes $\Omega({\rm OPT} /
\poly \log k)$ demand pairs with congestion at most
$14$, where OPT is the maximum number of pairs that can
be simultaneously routed on edge-disjoint paths. The
best previous algorithm that routed $\Omega({\rm OPT} /
\poly \log n)$ pairs required congestion $\poly(\log
\log n)$, and for the setting where the maximum allowed
congestion is bounded by a constant $c$, the best
previous algorithms could only guarantee the routing of
OPT / $n^{O(1/c)}$ pairs. We also introduce a new type
of vertex sparsifiers that we call integral flow
sparsifiers, which approximately preserve both
fractional and integral routings, and show an algorithm
to construct such sparsifiers.",
acknowledgement = ack-nhfb,
}
@InProceedings{An:2012:ICA,
author = "Hyung-Chan An and Robert Kleinberg and David B.
Shmoys",
title = "Improving {Christofides}' algorithm for the $s$-$t$
path {TSP}",
crossref = "ACM:2012:SPA",
pages = "875--886",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214055",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present a deterministic $(1 + \sqrt
5/2)$-approximation algorithm for the $s$-$t$ path TSP
for an arbitrary metric. Given a symmetric metric cost
on $n$ vertices including two prespecified endpoints,
the problem is to find a shortest Hamiltonian path
between the two endpoints; Hoogeveen showed that the
natural variant of Christofides' algorithm is a
$5/3$-approximation algorithm for this problem, and
this asymptotically tight bound in fact had been the
best approximation ratio known until now. We modify
this algorithm so that it chooses the initial spanning
tree based on an optimal solution to the Held--Karp
relaxation rather than a minimum spanning tree; we
prove this simple but crucial modification leads to an
improved approximation ratio, surpassing the
20-year-old barrier set by the natural Christofides'
algorithm variant. Our algorithm also proves an upper
bound of $1 + \sqrt 5/2$ on the integrality gap of the
path-variant Held--Karp relaxation. The techniques
devised in this paper can be applied to other
optimization problems as well: these applications
include improved approximation algorithms and improved
LP integrality gap upper bounds for the
prize-collecting $s$-$t$ path problem and the
unit-weight graphical metric $s$-$t$ path TSP.",
acknowledgement = ack-nhfb,
}
@InProceedings{Williams:2012:MMF,
author = "Virginia Vassilevska Williams",
title = "Multiplying matrices faster than
{Coppersmith--Winograd}",
crossref = "ACM:2012:SPA",
pages = "887--898",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214056",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We develop an automated approach for designing matrix
multiplication algorithms based on constructions
similar to the Coppersmith--Winograd construction.
Using this approach we obtain a new improved bound on
the matrix multiplication exponent $\omega < 2.3727$.",
acknowledgement = ack-nhfb,
keywords = "fast matrix multiplication",
}
@InProceedings{Coja-Oglan:2012:CKN,
author = "Amin Coja-Oglan and Konstantinos Panagiotou",
title = "Catching the {$k$-NAESAT} threshold",
crossref = "ACM:2012:SPA",
pages = "899--908",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214058",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The best current estimates of the thresholds for the
existence of solutions in random constraint
satisfaction problems ('CSPs') mostly derive from the
first and the second moment method. Yet apart from a
very few exceptional cases these methods do not quite
yield matching upper and lower bounds. According to
deep but non-rigorous arguments from statistical
mechanics, this discrepancy is due to a change in the
geometry of the set of solutions called condensation
that occurs shortly before the actual threshold for the
existence of solutions (Krzakala, Montanari,
Ricci-Tersenghi, Semerjian, Zdeborova: PNAS~2007). To
cope with condensation, physicists have developed a
sophisticated but non-rigorous formalism called Survey
Propagation (Mezard, Parisi, Zecchina: Science 2002).
This formalism yields precise conjectures on the
threshold values of many random CSPs. Here we develop a
new Survey Propagation inspired second moment method
for the random $k$-NAESAT problem, which is one of the
standard benchmark problems in the theory of random
CSPs. This new technique allows us to overcome the
barrier posed by condensation rigorously. We prove that
the threshold for the existence of solutions in random
$k$-NAESAT is $2^{k-1} \ln 2 - (\ln / 2 2 + 1/4) +
\epsilon_k$, where $|\epsilon_k| \leq 2^{-(1 -o
k(1))k}$, thereby verifying the statistical mechanics
conjecture for this problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cai:2012:CCC,
author = "Jin-Yi Cai and Xi Chen",
title = "Complexity of counting {CSP} with complex weights",
crossref = "ACM:2012:SPA",
pages = "909--920",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214059",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give a complexity dichotomy theorem for the
counting constraint satisfaction problem (\#CSP in
short) with algebraic complex weights. To this end, we
give three conditions for its tractability. Let $F$ be
any finite set of complex-valued functions. We show
that \#CSP($F$) is solvable in polynomial time if all
three conditions are satisfied; and is \#P-hard
otherwise. Our dichotomy theorem generalizes a long
series of important results on counting problems: (a)
the problem of counting graph homomorphisms is the
special case when $F$ has a single symmetric binary
function; (b) the problem of counting directed graph
homomorphisms is the special case when $F$ has a single
but not-necessarily-symmetric binary function; and (c)
the unweighted form of \#CSP is when all functions in
$F$ take values in $\{0, 1\}$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Molloy:2012:FTK,
author = "Michael Molloy",
title = "The freezing threshold for $k$-colourings of a random
graph",
crossref = "ACM:2012:SPA",
pages = "921--930",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214060",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We rigorously determine the exact freezing threshold,
$r_k^f$, for $k$-colourings of a random graph. We prove
that for random graphs with density above $r_k^f$,
almost every colouring is such that a linear number of
variables are {\em frozen}, meaning that their colours
cannot be changed by a sequence of alterations whereby
we change the colours of $o(n)$ vertices at a time,
always obtaining another proper colouring. When the
density is below $r_k^f$, then almost every colouring
has at most $o(n)$ frozen variables. This confirms
hypotheses made using the non-rigorous cavity
method.\par
It has been hypothesized that the freezing threshold is
the cause of the ``algorithmic barrier'', the long
observed phenomenon that when the edge-density of a
random graph exceeds $(1/2) k \ln k(1 + o_k(1))$, no
algorithms are known to find $k$-colourings, despite
the fact that this density is only half the
$k$-colourability threshold.\par
We also show that $r_k^f$ is the threshold of a strong
form of reconstruction for $k$-colourings of the
Galton--Watson tree, and of the graphical model.",
acknowledgement = ack-nhfb,
}
@InProceedings{Barto:2012:RSC,
author = "Libor Barto and Marcin Kozik",
title = "Robust satisfiability of constraint satisfaction
problems",
crossref = "ACM:2012:SPA",
pages = "931--940",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214061",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "An algorithm for a constraint satisfaction problem is
called robust if it outputs an assignment satisfying at
least $(1 - g(\epsilon))$-fraction of the constraints
given a $(1 - \epsilon)$-satisfiable instance, where
$g(\epsilon) \to 0$ as $\epsilon \to 0$, $g(0) = 0$.
Guruswami and Zhou conjectured a characterization of
constraint languages for which the corresponding
constraint satisfaction problem admits an efficient
robust algorithm. This paper confirms their
conjecture.",
acknowledgement = ack-nhfb,
}
@InProceedings{Woodruff:2012:TBD,
author = "David P. Woodruff and Qin Zhang",
title = "Tight bounds for distributed functional monitoring",
crossref = "ACM:2012:SPA",
pages = "941--960",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214063",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We resolve several fundamental questions in the area
of distributed functional monitoring, initiated by
Cormode, Muthukrishnan, and Yi (SODA, 2008), and
receiving recent attention. In this model there are $k$
sites each tracking their input streams and
communicating with a central coordinator. The
coordinator's task is to continuously maintain an
approximate output to a function computed over the
union of the $k$ streams. The goal is to minimize the
number of bits communicated. Let the $p$-th frequency
moment be defined as $F_p = \sum_i f_i^p$, where
$f_i$ is the frequency of element $i$. We show the
randomized communication complexity of estimating the
number of distinct elements (that is, $F_0$) up to a $1
+ \epsilon$ factor is $\Omega(k / \epsilon^2)$,
improving upon the previous $\Omega(k + 1/ \epsilon^2)$
bound and matching known upper bounds. For $F_p$, $p >
1$, we improve the previous $\Omega(k + 1/ \epsilon^2)$
communication bound to $\Omega(k^{p - 1} /
\epsilon^2)$. We obtain similar improvements for heavy
hitters, empirical entropy, and other problems. Our
lower bounds are the first of any kind in distributed
functional monitoring to depend on the product of $k$
and $1 / \epsilon^2$. Moreover, the lower bounds are
for the static version of the distributed functional
monitoring model where the coordinator only needs to
compute the function at the time when all $k$ input
streams end; surprisingly they almost match what is
achievable in the (dynamic version of) distributed
functional monitoring model where the coordinator needs
to keep track of the function continuously at any time
step. We also show that we can estimate $F_p$, for any
$p > 1$, using $O(k^{p - 1} \poly(\epsilon^{-1}))$
communication. This drastically improves upon the
previous $O(k^{2 p + 1} N^{1 - 2/p}
\poly(\epsilon^{-1}))$ bound of Cormode, Muthukrishnan,
and Yi for general $p$, and their $O(k^2 / \epsilon +
k^{1.5} / \epsilon^3)$ bound for $p = 2$. For $p = 2$,
our bound resolves their main open question. Our lower
bounds are based on new direct sum theorems for
approximate majority, and yield improvements to
classical problems in the standard data stream model.
First, we improve the known lower bound for estimating
$F_p$, $p > 2$, in $t$ passes from $\Omega(n^{1 - 2 /
p} /(\epsilon^{2 / p} t))$ to $\Omega(n^{1 - 2 / p}
/(\epsilon^{4 / p} t))$, giving the first bound that
matches what we expect when $p = 2$ for any constant
number of passes. Second, we give the first lower bound
for estimating $F_0$ in $t$ passes with $\Omega(1 /
(\epsilon^2 t))$ bits of space that does not use the
hardness of the gap-Hamming problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Censor-Hillel:2012:GCP,
author = "Keren Censor-Hillel and Bernhard Haeupler and Jonathan
Kelner and Petar Maymounkov",
title = "Global computation in a poorly connected world: fast
rumor spreading with no dependence on conductance",
crossref = "ACM:2012:SPA",
pages = "961--970",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214064",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In this paper, we study the question of how
efficiently a collection of interconnected nodes can
perform a global computation in the GOSSIP model of
communication. In this model, nodes do not know the
global topology of the network, and they may only
initiate contact with a single neighbor in each round.
This model contrasts with the much less restrictive
LOCAL model, where a node may simultaneously
communicate with all of its neighbors in a single
round. A basic question in this setting is how many
rounds of communication are required for the
information dissemination problem, in which each node
has some piece of information and is required to
collect all others. In the LOCAL model, this is quite
simple: each node broadcasts all of its information in
each round, and the number of rounds required will be
equal to the diameter of the underlying communication
graph. In the GOSSIP model, each node must
independently choose a single neighbor to contact, and
the lack of global information makes it difficult to
make any sort of principled choice. As such,
researchers have focused on the uniform gossip
algorithm, in which each node independently selects a
neighbor uniformly at random. When the graph is
well-connected, this works quite well. In a string of
beautiful papers, researchers proved a sequence of
successively stronger bounds on the number of rounds
required in terms of the conductance $\phi$ and graph
size $n$, culminating in a bound of $O(\phi^{-1} \log
n)$. In this paper, we show that a fairly simple
modification of the protocol gives an algorithm that
solves the information dissemination problem in at most
$O(D + \polylog(n))$ rounds in a network of diameter
$D$, with no dependence on the conductance. This is at
most an additive polylogarithmic factor from the
trivial lower bound of $D$, which applies even in the
LOCAL model. In fact, we prove that something stronger
is true: any algorithm that requires $T$ rounds in the
LOCAL model can be simulated in $O(T + \polylog(n))$
rounds in the GOSSIP model. We thus prove that these
two models of distributed computation are essentially
equivalent.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bansal:2012:TTS,
author = "Nikhil Bansal and Vibhor Bhatt and Prasad Jayanti and
Ranganath Kondapally",
title = "Tight time-space tradeoff for mutual exclusion",
crossref = "ACM:2012:SPA",
pages = "971--982",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214065",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Mutual Exclusion is a fundamental problem in
distributed computing, and the problem of proving upper
and lower bounds on the RMR complexity of this problem
has been extensively studied. Here, we give matching
lower and upper bounds on how RMR complexity trades off
with space. Two implications of our results are that
constant RMR complexity is impossible with
subpolynomial space and subpolynomial RMR complexity is
impossible with constant space for cache-coherent
multiprocessors, regardless of how strong the hardware
synchronization operations are. To prove these results
we show that the complexity of mutual exclusion, which
can be ``messy'' to analyze because of system details
such as asynchrony and cache coherence, is captured
precisely by a simple and purely combinatorial game
that we design. We then derive lower and upper bounds
for this game, thereby obtaining corresponding bounds
for mutual exclusion. The lower bounds for the game are
proved using potential functions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Giakkoupis:2012:TRL,
author = "George Giakkoupis and Philipp Woelfel",
title = "A tight {RMR} lower bound for randomized mutual
exclusion",
crossref = "ACM:2012:SPA",
pages = "983--1002",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214066",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The Cache Coherent (CC) and the Distributed Shared
Memory (DSM) models are standard shared memory models,
and the Remote Memory Reference (RMR) complexity is
considered to accurately predict the actual performance
of mutual exclusion algorithms in shared memory
systems. In this paper we prove a tight lower bound for
the RMR complexity of deadlock-free randomized mutual
exclusion algorithms in both the CC and the DSM model
with atomic registers and compare \& swap objects and
an adaptive adversary. Our lower bound establishes that
an adaptive adversary can schedule $n$ processes in
such a way that each enters the critical section once,
and the total number of RMRs is $\Omega(n \log n/\log
\log n)$ in expectation. This matches an upper bound of
Hendler and Woelfel (2011).",
acknowledgement = ack-nhfb,
}
@InProceedings{Garg:2012:CPA,
author = "Jugal Garg and Ruta Mehta and Milind Sohoni and Vijay
V. Vazirani",
title = "A complementary pivot algorithm for markets under
separable, piecewise-linear concave utilities",
crossref = "ACM:2012:SPA",
pages = "1003--1016",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214068",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Using the powerful machinery of the linear
complementarity problem and Lemke's algorithm, we give
a practical algorithm for computing an equilibrium for
Arrow--Debreu markets under separable, piecewise-linear
concave (SPLC) utilities, despite the PPAD-completeness
of this case. As a corollary, we obtain the first
elementary proof of existence of equilibrium for this
case, i.e., without using fixed point theorems. In
1975, Eaves [10] had given such an algorithm for the
case of linear utilities and had asked for an extension
to the piecewise-linear, concave utilities. Our result
settles the relevant subcase of his problem as well as
the problem of Vazirani and Yannakakis of obtaining a
path following algorithm for SPLC markets, thereby
giving a direct proof of membership of this case in
PPAD. We also prove that SPLC markets have an odd
number of equilibria (up to scaling), hence matching
the classical result of Shapley about 2-Nash equilibria
[24], which was based on the Lemke--Howson algorithm.
For the linear case, Eaves had asked for a
combinatorial interpretation of his algorithm. We
provide this and it yields a particularly simple proof
of the fact that the set of equilibrium prices is
convex.",
acknowledgement = ack-nhfb,
}
@InProceedings{Azar:2012:RP,
author = "Pablo Daniel Azar and Silvio Micali",
title = "Rational proofs",
crossref = "ACM:2012:SPA",
pages = "1017--1028",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214069",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study a new type of proof system, where an
unbounded prover and a polynomial time verifier
interact, on inputs a string $x$ and a function $f$, so
that the Verifier may learn $f(x)$. The novelty of our
setting is that there no longer are ``good'' or
``malicious'' provers, but only rational ones. In
essence, the Verifier has a budget $c$ and gives the
Prover a reward $r \in [0,c]$ determined by the
transcript of their interaction; the prover wishes to
maximize his expected reward; and his reward is
maximized only if he the verifier correctly learns
$f(x)$. Rational proof systems are as powerful as their
classical counterparts for polynomially many rounds of
interaction, but are much more powerful when we only
allow a constant number of rounds. Indeed, we prove
that if $f \in \#P$, then $f$ is computable by a
one-round rational Merlin--Arthur game, where, on input
$x$, Merlin's single message actually consists of
sending just the value $f(x)$. Further, we prove that
CH, the counting hierarchy, coincides with the class of
languages computable by a constant-round rational
Merlin--Arthur game. Our results rely on a basic and
crucial connection between rational proof systems and
proper scoring rules, a tool developed to elicit
truthful information from experts.",
acknowledgement = ack-nhfb,
}
@InProceedings{Abernethy:2012:MOP,
author = "Jacob Abernethy and Rafael M. Frongillo and Andre
Wibisono",
title = "Minimax option pricing meets {Black--Scholes} in the
limit",
crossref = "ACM:2012:SPA",
pages = "1029--1040",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214070",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Option contracts are a type of financial derivative
that allow investors to hedge risk and speculate on the
variation of an asset's future market price. In short,
an option has a particular payout that is based on the
market price for an asset on a given date in the
future. In 1973, Black and Scholes proposed a valuation
model for options that essentially estimates the tail
risk of the asset price under the assumption that the
price will fluctuate according to geometric Brownian
motion. A key element of their analysis is that the
investor can ``hedge'' the payout of the option by
continuously buying and selling the asset depending on
the price fluctuations. More recently, DeMarzo et al.
proposed a more robust valuation scheme which does not
require any assumption on the price path; indeed, in
their model the asset's price can even be chosen
adversarially. This framework can be considered as a
sequential two-player zero-sum game between the
investor and Nature. We analyze the value of this game
in the limit, where the investor can trade at smaller
and smaller time intervals. Under weak assumptions on
the actions of Nature (an adversary), we show that the
minimax option price asymptotically approaches exactly
the Black--Scholes valuation. The key piece of our
analysis is showing that Nature's minimax optimal dual
strategy converges to geometric Brownian motion in the
limit.",
acknowledgement = ack-nhfb,
}
@InProceedings{Mossel:2012:QGS,
author = "Elchanan Mossel and Mikl{\'o}s Z. R{\'a}cz",
title = "A quantitative {Gibbard--Satterthwaite} theorem
without neutrality",
crossref = "ACM:2012:SPA",
pages = "1041--1060",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214071",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Recently, quantitative versions of the
Gibbard--Satterthwaite theorem were proven for $k = 3$
alternatives by Friedgut, Kalai, Keller and Nisan and
for neutral functions on $k \geq 4$ alternatives by
Isaksson, Kindler and Mossel. In the present paper we
prove a quantitative version of the
Gibbard--Satterthwaite theorem for general social
choice functions for any number $k \geq 3$ of
alternatives. In particular we show that for a social
choice function $f$ on $k \geq 3$ alternatives and $n$
voters, which is $\epsilon$-far from the family of
nonmanipulable functions, a uniformly chosen voter
profile is manipulable with probability at least
inverse polynomial in $n$, $k$, and $\epsilon^{-1}$.
Removing the neutrality assumption of previous theorems
is important for multiple reasons. For one, it is known
that there is a conflict between anonymity and
neutrality, and since most common voting rules are
anonymous, they cannot always be neutral. Second,
virtual elections are used in many applications in
artificial intelligence, where there are often
restrictions on the outcome of the election, and so
neutrality is not a natural assumption in these
situations. Ours is a unified proof which in particular
covers all previous cases established before. The proof
crucially uses reverse hypercontractivity in addition
to several ideas from the two previous proofs. Much of
the work is devoted to understanding functions of a
single voter, and in particular we also prove a
quantitative Gibbard--Satterthwaite theorem for one
voter.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bourgain:2012:ME,
author = "Jean Bourgain and Amir Yehudayoff",
title = "Monotone expansion",
crossref = "ACM:2012:SPA",
pages = "1061--1078",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214073",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "This work presents an explicit construction of a
family of monotone expanders, which are bi-partite
expander graphs whose edge-set is defined by (partial)
monotone functions. The family is essentially defined
by the M{\"o}bius action of ${\rm SL}_2(R)$, the group
of $2 \times 2$ matrices with determinant one, on the
interval $[0, 1]$. No other proof-of-existence for
monotone expanders is known, not even using the
probabilistic method. The proof extends recent results
on finite/compact groups to the non-compact scenario.
Specifically, we show a product-growth theorem for
${\rm SL}_2(R)$; roughly, that for every $A \subset
{\rm SL}_2(R)$ with certain properties, the size of
$AAA$ is much larger than that of $A$. We mention two
applications of this construction: Dvir and Shpilka
showed that it yields a construction of explicit
dimension expanders, which are a generalization of
standard expander graphs. Dvir and Wigderson proved
that it yields the existence of explicit pushdown
expanders, which are graphs that arise in Turing
machine simulations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Alon:2012:NCG,
author = "Noga Alon and Ankur Moitra and Benny Sudakov",
title = "Nearly complete graphs decomposable into large induced
matchings and their applications",
crossref = "ACM:2012:SPA",
pages = "1079--1090",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214074",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We describe two constructions of (very) dense graphs
which are edge disjoint unions of large {\em induced\/}
matchings. The first construction exhibits graphs on
$N$ vertices with ${N \choose 2} - o(N^2)$ edges, which
can be decomposed into pairwise disjoint induced
matchings, each of size $N^{1 - o(1)}$. The second
construction provides a covering of all edges of the
complete graph $K_N$ by two graphs, each being the edge
disjoint union of at most $N^{2 - \delta}$ induced
matchings, where $\delta > 0.076$. This disproves (in a
strong form) a conjecture of Meshulam, substantially
improves a result of Birk, Linial and Meshulam on
communicating over a shared channel, and (slightly)
extends the analysis of Hastad and Wigderson of the
graph test of Samorodnitsky and Trevisan for linearity.
Additionally, our constructions settle a combinatorial
question of Vempala regarding a candidate rounding
scheme for the directed Steiner tree problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kuperberg:2012:PER,
author = "Greg Kuperberg and Shachar Lovett and Ron Peled",
title = "Probabilistic existence of rigid combinatorial
structures",
crossref = "ACM:2012:SPA",
pages = "1091--1106",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214075",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We show the existence of rigid combinatorial objects
which previously were not known to exist. Specifically,
for a wide range of the underlying parameters, we show
the existence of non-trivial orthogonal arrays,
$t$-designs, and $t$-wise permutations. In all cases,
the sizes of the objects are optimal up to polynomial
overhead. The proof of existence is probabilistic. We
show that a randomly chosen such object has the
required properties with positive yet tiny probability.
The main technical ingredient is a special local
central limit theorem for suitable lattice random walks
with finitely many steps.",
acknowledgement = ack-nhfb,
}
@InProceedings{Dobzinski:2012:QCC,
author = "Shahar Dobzinski and Jan Vondrak",
title = "From query complexity to computational complexity",
crossref = "ACM:2012:SPA",
pages = "1107--1116",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214076",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider submodular optimization problems, and
provide a general way of translating oracle
inapproximability results arising from the symmetry gap
technique to computational complexity inapproximability
results, where the submodular function is given
explicitly (under the assumption that NP $\not=$ RP).
Applications of our technique include an optimal
computational hardness of $(1/2 +
\epsilon)$-approximation for maximizing a symmetric
nonnegative submodular function, an optimal hardness of
$(1 - (1 - 1 / k)^k + \epsilon)$-approximation for
welfare maximization in combinatorial auctions with $k$
submodular bidders (for constant $k$), super-constant
hardness for maximizing a nonnegative submodular
function over matroid bases, and tighter bounds for
maximizing a monotone submodular function subject to a
cardinality constraint. Unlike the vast majority of
computational inapproximability results, our approach
does not use the PCP machinery or the Unique Games
Conjecture, but relies instead on a direct reduction
from Unique-SAT using list-decodable codes.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lee:2012:MWS,
author = "James R. Lee and Shayan Oveis Gharan and Luca
Trevisan",
title = "Multi-way spectral partitioning and higher-order
{Cheeger} inequalities",
crossref = "ACM:2012:SPA",
pages = "1117--1130",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214078",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A basic fact in spectral graph theory is that the
number of connected components in an undirected graph
is equal to the multiplicity of the eigenvalue zero in
the Laplacian matrix of the graph. In particular, the
graph is disconnected if and only if there are at least
two eigenvalues equal to zero. Cheeger's inequality and
its variants provide an approximate version of the
latter fact; they state that a graph has a sparse cut
if and only if there are at least two eigenvalues that
are close to zero. It has been conjectured that an
analogous characterization holds for higher
multiplicities, i.e., there are $k$ eigenvalues close
to zero if and only if the vertex set can be
partitioned into $k$ subsets, each defining a sparse
cut. We resolve this conjecture. Our result provides a
theoretical justification for clustering algorithms
that use the bottom $k$ eigenvectors to embed the
vertices into R$^k$, and then apply geometric
considerations to the embedding. We also show that
these techniques yield a nearly optimal quantitative
connection between the expansion of sets of size
$\approx n/k$ and $\lambda_k$, the $k$th smallest
eigenvalue of the normalized Laplacian, where $n$ is
the number of vertices. In particular, we show that in
every graph there are at least $k / 2$ disjoint sets
(one of which will have size at most $2 n / k$), each
having expansion at most $O(\sqrt{\lambda_k \log k})$.
Louis, Raghavendra, Tetali, and Vempala have
independently proved a slightly weaker version of this
last result [LRTV12]. The $\sqrt{\log k}$ bound is
tight, up to constant factors, for the ``noisy
hypercube'' graphs.",
acknowledgement = ack-nhfb,
}
@InProceedings{Louis:2012:MSC,
author = "Anand Louis and Prasad Raghavendra and Prasad Tetali
and Santosh Vempala",
title = "Many sparse cuts via higher eigenvalues",
crossref = "ACM:2012:SPA",
pages = "1131--1140",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214079",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Cheeger's fundamental inequality states that any
edge-weighted graph has a vertex subset $S$ such that
its expansion (a.k.a. conductance) is bounded as
follows:\par
$$\phi(S) {\hbox{\tiny \rm def} \atop =} (w(S,
\bar{S})) / \min \{w(S), w(\bar{S})\} \leq \sqrt{2
\lambda_2}$$\par
where $w$ is the total edge weight of a subset or a cut
and $\lambda_2$ is the second smallest eigenvalue of
the normalized Laplacian of the graph. Here we prove
the following natural generalization: for any integer
$k \in [n]$, there exist $c k$ disjoint subsets $S_1$,
\ldots{}, $S_{c k}$, such that\par
$$\max_i \phi(S_i) \leq C \sqrt{\lambda_k \log
k}$$\par
where $\lambda_k$ is the $k$th smallest eigenvalue of
the normalized Laplacian and $c < 1$, $C > 0$ are
suitable absolute constants. Our proof is via a
polynomial-time algorithm to find such subsets,
consisting of a spectral projection and a randomized
rounding. As a consequence, we get the same upper bound
for the small set expansion problem, namely for any
$k$, there is a subset $S$ whose weight is at most a
$O(1/k)$ fraction of the total weight and $\phi(S) \leq
C \sqrt{\lambda_k \log k}$. Both results are the best
possible up to constant factors.\par
The underlying algorithmic problem, namely finding $k$
subsets such that the maximum expansion is minimized,
besides extending sparse cuts to more than one subset,
appears to be a natural clustering problem in its own
right.",
acknowledgement = ack-nhfb,
}
@InProceedings{Orecchia:2012:AEL,
author = "Lorenzo Orecchia and Sushant Sachdeva and Nisheeth K.
Vishnoi",
title = "Approximating the exponential, the {Lanczos} method
and an {$\tilde{O}(m)$}-time spectral algorithm for
balanced separator",
crossref = "ACM:2012:SPA",
pages = "1141--1160",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214080",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give a novel spectral approximation algorithm for
the balanced (edge-)separator problem that, given a
graph $G$, a constant balance $b \in (0,1/2]$, and a
parameter $\gamma$, either finds an
$\Omega(b)$-balanced cut of conductance $O(\sqrt
\gamma)$ in $G$, or outputs a certificate that all
$b$-balanced cuts in $G$ have conductance at least
$\gamma$, and runs in time $\tilde{O}(m)$. This settles
the question of designing asymptotically optimal
spectral algorithms for balanced separator. Our
algorithm relies on a variant of the heat kernel random
walk and requires, as a subroutine, an algorithm to
compute $\exp(-L) v$ where $L$ is the Laplacian of a
graph related to $G$ and $v$ is a vector. Algorithms
for computing the matrix-exponential-vector product
efficiently comprise our next set of results. Our main
result here is a new algorithm which computes a good
approximation to $\exp(-A) v$ for a class of symmetric
positive semidefinite (PSD) matrices $A$ and a given
vector $v$, in time roughly $\tilde{O}(m_A)$,
independent of the norm of $A$, where $m_A$ is the
number of non-zero entries of $A$. This uses, in a
non-trivial way, the result of Spielman and Teng on
inverting symmetric and diagonally-dominant matrices in
$\tilde{O}(m_A)$ time. Finally, using old and new
uniform approximations to $e^{-x}$ we show how to
obtain, via the Lanczos method, a simple algorithm to
compute $\exp(-A) v$ for symmetric PSD matrices that
runs in time roughly $O(t_A \cdot \sqrt{\norm(A)})$,
where $t_A$ is the time required for the computation of
the vector $A w$ for given vector w. As an application,
we obtain a simple and practical algorithm, with output
conductance $O(\sqrt \gamma)$, for balanced separator
that runs in time $O(m / \sqrt \gamma)$. This latter
algorithm matches the running time, but improves on the
approximation guarantee of the Evolving-Sets-based
algorithm by Andersen and Peres for balanced
separator.",
acknowledgement = ack-nhfb,
}
@InProceedings{Goemans:2012:MIG,
author = "Michel X. Goemans and Neil Olver and Thomas
Rothvo{\ss} and Rico Zenklusen",
title = "Matroids and integrality gaps for hypergraphic
{Steiner} tree relaxations",
crossref = "ACM:2012:SPA",
pages = "1161--1176",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214081",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Until recently, LP relaxations have only played a very
limited role in the design of approximation algorithms
for the Steiner tree problem. In particular, no
(efficiently solvable) Steiner tree relaxation was
known to have an integrality gap bounded away from $2$,
before Byrka et al. [3] showed an upper bound of
$\approx 1.55$ of a hypergraphic LP relaxation and
presented a $\ln(4) + \epsilon \approx 1.39$
approximation based on this relaxation. Interestingly,
even though their approach is LP based, they do not
compare the solution produced against the LP
value.\par
We take a fresh look at hypergraphic LP relaxations for
the Steiner tree problem --- one that heavily exploits
methods and results from the theory of matroids and
submodular functions --- which leads to stronger
integrality gaps, faster algorithms, and a variety of
structural insights of independent interest. More
precisely, along the lines of the algorithm of Byrka et
al.[3], we present a deterministic $\ln(4) + \epsilon$
approximation that compares against the LP value and
therefore proves a matching $\ln(4)$ upper bound on the
integrality gap of hypergraphic
relaxations.\par
Similarly to [3], we iteratively fix one component and
update the LP solution. However, whereas in [3] the LP
is solved at every iteration after contracting a
component, we show how feasibility can be maintained by
a greedy procedure on a well-chosen matroid. Apart from
avoiding the expensive step of solving a hypergraphic
LP at each iteration, our algorithm can be analyzed
using a simple potential function. This potential
function gives an easy means to determine stronger
approximation guarantees and integrality gaps when
considering restricted graph topologies. In particular,
this readily leads to a $73/60 \approx 1.217$ upper
bound on the integrality gap of hypergraphic
relaxations for quasi-bipartite
graphs.\par
Additionally, for the case of quasi-bipartite graphs,
we present a simple algorithm to transform an optimal
solution to the bidirected cut relaxation to an optimal
solution of the hypergraphic relaxation, leading to a
fast $73/60$ approximation for quasi-bipartite graphs.
Furthermore, we show how the separation problem of the
hypergraphic relaxation can be solved by computing
maximum flows, which provides a way to obtain a fast
independence oracle for the matroids that we use in our
approach.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brodal:2012:SFH,
author = "Gerth St{\o}lting Brodal and George Lagogiannis and
Robert E. Tarjan",
title = "Strict {Fibonacci} heaps",
crossref = "ACM:2012:SPA",
pages = "1177--1184",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214082",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present the first pointer-based heap implementation
with time bounds matching those of Fibonacci heaps in
the worst case. We support make-heap, insert, find-min,
meld and decrease-key in worst-case $O(1)$ time, and
delete and delete-min in worst-case $O(\lg n)$ time,
where $n$ is the size of the heap. The data structure
uses linear space. A previous, very complicated,
solution achieving the same time bounds in the RAM
model made essential use of arrays and extensive use of
redundant counter schemes to maintain balance. Our
solution uses neither. Our key simplification is to
discard the structure of the smaller heap when doing a
meld. We use the pigeonhole principle in place of the
redundant counter mechanism.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bulnek:2012:TLB,
author = "Jan Bul{\'a}nek and Michal Kouck{\'y} and Michael
Saks",
title = "Tight lower bounds for the online labeling problem",
crossref = "ACM:2012:SPA",
pages = "1185--1198",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214083",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider the file maintenance problem (also called
the online labeling problem) in which $n$ integer items
from the set $\{1, \ldots{}, r\}$ are to be stored in
an array of size $m \geq n$. The items are presented
sequentially in an arbitrary order, and must be stored
in the array in sorted order (but not necessarily in
consecutive locations in the array). Each new item must
be stored in the array before the next item is
received. If $r \leq m$ then we can simply store item
$j$ in location $j$ but if $r > m$ then we may have to
shift the location of stored items to make space for a
newly arrived item. The algorithm is charged each time
an item is stored in the array, or moved to a new
location. The goal is to minimize the total number of
such moves the algorithm has to do. This problem is
non-trivial when $n \leq m < r$. In the case that $m =
Cn$ for some $C > 1$, algorithms for this problem with
cost $O(\log(n)^2)$ per item have been given [Itai et
al. (1981), Willard (1992), Bender et al. (2002)]. When
$m = n$, algorithms with cost $O(\log(n)^3)$ per item
were given [Zhang (1993),Bird and Sadnicki (2007)]. In
this paper we prove lower bounds that show that these
algorithms are optimal, up to constant factors.
Previously, the only lower bound known for this range
of parameters was a lower bound of $\Omega(\log(n)^2)$
for the restricted class of smooth algorithms [Dietz et
al. (2005), Zhang (1993)]. We also provide an algorithm
for the sparse case: If the number of items is
polylogarithmic in the array size then the problem can
be solved in amortized constant time per item.",
acknowledgement = ack-nhfb,
}
@InProceedings{Abraham:2012:FDA,
author = "Ittai Abraham and Shiri Chechik and Cyril Gavoille",
title = "Fully dynamic approximate distance oracles for planar
graphs via forbidden-set distance labels",
crossref = "ACM:2012:SPA",
pages = "1199--1218",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214084",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "This paper considers fully dynamic $(1 + \epsilon)$
distance oracles and $(1 + \epsilon)$ forbidden-set
labeling schemes for planar graphs. For a given
$n$-vertex planar graph $G$ with edge weights drawn
from $[1,M]$ and parameter $\epsilon > 0$, our
forbidden-set labeling scheme uses labels of length
$\lambda = O(\epsilon^{-1} \log^2 n \log (n M) \cdot
\log n)$. Given the labels of two vertices $s$ and $t$
and of a set $F$ of faulty vertices\slash edges, our
scheme approximates the distance between $s$ and $t$ in
$G \backslash F$ with stretch $(1 + \epsilon)$, in
$O(|F|^2 \lambda)$ time.\par
We then present a general method to transform $(1 +
\epsilon)$ forbidden-set labeling schemas into a fully
dynamic $(1 + \epsilon)$ distance oracle. Our fully
dynamic $(1 + \epsilon)$ distance oracle is of size
$O(n \log n \cdot (\epsilon^{-1} + \log n))$ and has
$\tilde{O}(n^{1/2})$ query and update time, both the
query and the update time are worst case. This improves
on the best previously known $(1 + \epsilon)$ dynamic
distance oracle for planar graphs, which has worst case
query time $\tilde{O}(n^{2/3})$ and amortized update
time of $\tilde{O}(n^{2/3})$.\par
Our $(1 + \epsilon)$ forbidden-set labeling scheme can
also be extended into a forbidden-set labeled routing
scheme with stretch $(1 + \epsilon)$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lopez-Alt:2012:FMC,
author = "Adriana L{\'o}pez-Alt and Eran Tromer and Vinod
Vaikuntanathan",
title = "On-the-fly multiparty computation on the cloud via
multikey fully homomorphic encryption",
crossref = "ACM:2012:SPA",
pages = "1219--1234",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214086",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We propose a new notion of secure multiparty
computation aided by a computationally-powerful but
untrusted ``cloud'' server. In this notion that we call
on-the-fly multiparty computation (MPC), the cloud can
non-interactively perform arbitrary, dynamically chosen
computations on data belonging to arbitrary sets of
users chosen on-the-fly. All user's input data and
intermediate results are protected from snooping by the
cloud as well as other users. This extends the standard
notion of fully homomorphic encryption (FHE), where
users can only enlist the cloud's help in evaluating
functions on their own encrypted data. In on-the-fly
MPC, each user is involved only when initially
uploading his (encrypted) data to the cloud, and in a
final output decryption phase when outputs are
revealed; the complexity of both is independent of the
function being computed and the total number of users
in the system. When users upload their data, they need
not decide in advance which function will be computed,
nor who they will compute with; they need only
retroactively approve the eventually-chosen functions
and on whose data the functions were evaluated. This
notion is qualitatively the best possible in minimizing
interaction, since the users' interaction in the
decryption stage is inevitable: we show that removing
it would imply generic program obfuscation and is thus
impossible. Our contributions are two-fold:- We show
how on-the-fly MPC can be achieved using a new type of
encryption scheme that we call multikey FHE, which is
capable of operating on inputs encrypted under
multiple, unrelated keys. A ciphertext resulting from a
multikey evaluation can be jointly decrypted using the
secret keys of all the users involved in the
computation. --- We construct a multikey FHE scheme
based on NTRU, a very efficient public-key encryption
scheme proposed in the 1990s. It was previously not
known how to make NTRU fully homomorphic even for a
single party. We view the construction of (multikey)
FHE from NTRU encryption as a main contribution of
independent interest. Although the transformation to a
fully homomorphic system deteriorates the efficiency of
NTRU somewhat, we believe that this system is a leading
candidate for a practical FHE scheme.",
acknowledgement = ack-nhfb,
}
@InProceedings{Boyle:2012:MCS,
author = "Elette Boyle and Shafi Goldwasser and Abhishek Jain
and Yael Tauman Kalai",
title = "Multiparty computation secure against continual memory
leakage",
crossref = "ACM:2012:SPA",
pages = "1235--1254",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214087",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We construct a multiparty computation (MPC) protocol
that is secure even if a malicious adversary, in
addition to corrupting $1 - \epsilon$ fraction of all
parties for an arbitrarily small constant $\epsilon >
0$, can leak information about the secret state of each
honest party. This leakage can be continuous for an
unbounded number of executions of the MPC protocol,
computing different functions on the same or different
set of inputs. We assume a (necessary) ``leak-free''
preprocessing stage. We emphasize that we achieve
leakage resilience without weakening the security
guarantee of classical MPC. Namely, an adversary who is
given leakage on honest parties' states, is guaranteed
to learn nothing beyond the input and output values of
corrupted parties. This is in contrast with previous
works on leakage in the multi-party protocol setting,
which weaken the security notion, and only guarantee
that a protocol which leaks $l$ bits about the parties'
secret states, yields at most $l$ bits of leakage on
the parties' private inputs. For some functions, such
as voting, such leakage can be detrimental. Our result
relies on standard cryptographic assumptions, and our
security parameter is polynomially related to the
number of parties.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hardt:2012:BRR,
author = "Moritz Hardt and Aaron Roth",
title = "Beating randomized response on incoherent matrices",
crossref = "ACM:2012:SPA",
pages = "1255--1268",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214088",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Computing accurate low rank approximations of large
matrices is a fundamental data mining task. In many
applications however the matrix contains sensitive
information about individuals. In such case we would
like to release a low rank approximation that satisfies
a strong privacy guarantee such as differential
privacy. Unfortunately, to date the best known
algorithm for this task that satisfies differential
privacy is based on naive input perturbation or
randomized response: Each entry of the matrix is
perturbed independently by a sufficiently large random
noise variable, a low rank approximation is then
computed on the resulting matrix. We give (the first)
significant improvements in accuracy over randomized
response under the natural and necessary assumption
that the matrix has low coherence. Our algorithm is
also very efficient and finds a constant rank
approximation of an $m \times n$ matrix in time $O(m
n)$. Note that even generating the noise matrix
required for randomized response already requires time
$O(mn)$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bhaskara:2012:UDP,
author = "Aditya Bhaskara and Daniel Dadush and Ravishankar
Krishnaswamy and Kunal Talwar",
title = "Unconditional differentially private mechanisms for
linear queries",
crossref = "ACM:2012:SPA",
pages = "1269--1284",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214089",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We investigate the problem of designing differentially
private mechanisms for a set of $d$ linear queries over
a database, while adding as little error as possible.
Hardt and Talwar [HT10] related this problem to
geometric properties of a convex body defined by the
set of queries and gave a $O(\log^3 d)$-approximation
to the minimum $l_2^2$ error, assuming a conjecture
from convex geometry called the Slicing or Hyperplane
conjecture. In this work we give a mechanism that works
unconditionally, and also gives an improved $O(\log^2
d)$ approximation to the expected $l_2^2$ error. We
remove the dependence on the Slicing conjecture by
using a result of Klartag [Kla06] that shows that any
convex body is close to one for which the conjecture
holds; our main contribution is in making this result
constructive by using recent techniques of Dadush,
Peikert and Vempala [DPV10]. The improvement in
approximation ratio relies on a stronger lower bound we
derive on the optimum. This new lower bound goes beyond
the packing argument that has traditionally been used
in Differential Privacy and allows us to add the
packing lower bounds obtained from orthogonal
subspaces. We are able to achieve this via a
symmetrization argument which argues that there always
exists a near optimal differentially private mechanism
which adds noise that is independent of the input
database! We believe this result should be of
independent interest, and also discuss some interesting
consequences.",
acknowledgement = ack-nhfb,
}
@InProceedings{Muthukrishnan:2012:OPH,
author = "S. Muthukrishnan and Aleksandar Nikolov",
title = "Optimal private halfspace counting via discrepancy",
crossref = "ACM:2012:SPA",
pages = "1285--1292",
year = "2012",
DOI = "https://doi.org/10.1145/2213977.2214090",
bibdate = "Thu Nov 8 19:11:58 MST 2012",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A {\em range counting\/} problem is specified by a set
$P$ of size $|P| = n$ of points in $\mathbb{R}^d$, an
integer {\em weight\/} $x_p$ associated to each point
$p \in P$, and a {\em range space\/} ${\cal R}
\subseteq 2^P$. Given a query range $R \in {\cal R}$,
the output is $R(x) = \sum_{p \in R} x_p$. The {\em
average squared error\/} of an algorithm ${\cal A}$ is
$1/|R| \sum_{R \in {\cal R}} ({\cal A}(R, x) -
R(x))^2$. Range counting for different range spaces is
a central problem in Computational Geometry.\par
We study $(\epsilon, \delta)$-differentially private
algorithms for range counting. Our main results are for
the range space given by hyperplanes, that is, the
halfspace counting problem. We present an $(\epsilon,
\delta)$-differentially private algorithm for halfspace
counting in $d$ dimensions which is $O(n^{1 - 1/d})$
approximate for average squared error. This contrasts
with the $\Omega(n)$ lower bound established by the
classical result of Dinur and Nissim on approximation
for arbitrary subset counting queries. We also show a
matching lower bound of $\Omega(n^{1 - 1 /d})$
approximation for any $(\epsilon,
\delta)$-differentially private algorithm for halfspace
counting.\par
Both bounds are obtained using discrepancy theory. For
the lower bound, we use a modified discrepancy measure
and bound approximation of $(\epsilon,
\delta)$-differentially private algorithms for range
counting queries in terms of this discrepancy. We also
relate the modified discrepancy measure to classical
combinatorial discrepancy, which allows us to exploit
known discrepancy lower bounds. This approach also
yields a lower bound of $\Omega((\log n)^{d - 1})$ for
$(\epsilon, \delta)$-differentially private {\em
orthogonal\/} range counting in $d$ dimensions, the
first known superconstant lower bound for this problem.
For the upper bound, we use an approach inspired by
partial coloring methods for proving discrepancy upper
bounds, and obtain $(\epsilon, \delta)$-differentially
private algorithms for range counting with polynomially
bounded shatter function range spaces.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kane:2013:PLF,
author = "Daniel M. Kane and Raghu Meka",
title = "A {PRG} for {Lipschitz} functions of polynomials with
applications to sparsest cut",
crossref = "ACM:2013:SPF",
pages = "1--10",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488610",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give improved pseudorandom generators (PRGs) for
Lipschitz functions of low-degree polynomials over the
hypercube. These are functions of the form $ \psi
(P(x)) $, where $ P : {1, - 1}^n \to R $ is a
low-degree polynomial and $ \psi : R \to R $ is a
function with small Lipschitz constant. PRGs for smooth
functions of low-degree polynomials have received a lot
of attention recently and play an important role in
constructing PRGs for the natural class of polynomial
threshold functions [12,13,24,16,15]. In spite of the
recent progress, no nontrivial PRGs were known for
fooling Lipschitz functions of degree $ O(\log n) $
polynomials even for constant error rate. In this work,
we give the first such generator obtaining a
seed-length of $ (\log n) O(l^2 / \epsilon^2) $ for
fooling degree $l$ polynomials with error $ \epsilon $.
Previous generators had an exponential dependence on
the degree $l$. We use our PRG to get better
integrality gap instances for sparsest cut, a
fundamental problem in graph theory with many
applications in graph optimization. We give an instance
of uniform sparsest cut for which a powerful
semi-definite relaxation (SDP) first introduced by
Goemans and Linial and studied in the seminal work of
Arora, Rao and Vazirani [3] has an integrality gap of $
\exp (\Omega ((\log \log n)^{1 / 2})) $. Understanding
the performance of the Goemans--Linial SDP for uniform
sparsest cut is an important open problem in
approximation algorithms and metric embeddings. Our
work gives a near-exponential improvement over previous
lower bounds which achieved a gap of $ \Omega (\log
\log n) $ [11,21]. Our gap instance builds on the
recent short code gadgets of Barak et al. [5].",
acknowledgement = ack-nhfb,
}
@InProceedings{Kwok:2013:ICI,
author = "Tsz Chiu Kwok and Lap Chi Lau and Yin Tat Lee and
Shayan Oveis Gharan and Luca Trevisan",
title = "Improved {Cheeger}'s inequality: analysis of spectral
partitioning algorithms through higher order spectral
gap",
crossref = "ACM:2013:SPF",
pages = "11--20",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488611",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Let $ \phi (G) $ be the minimum conductance of an
undirected graph $G$, and let $ 0 = \lambda_1 \leq
\lambda_2 \leq \ldots {} \leq \lambda_n \leq 2 $ be the
eigenvalues of the normalized Laplacian matrix of $G$.
We prove that for any graph $G$ and any $ k \geq 2 $, $
[\phi (G) = O(k) l_2 / \sqrt l_k] $, and this
performance guarantee is achieved by the spectral
partitioning algorithm. This improves Cheeger's
inequality, and the bound is optimal up to a constant
factor for any $k$. Our result shows that the spectral
partitioning algorithm is a constant factor
approximation algorithm for finding a sparse cut if $
l_k $ is a constant for some constant $k$. This
provides some theoretical justification to its
empirical performance in image segmentation and
clustering problems. We extend the analysis to spectral
algorithms for other graph partitioning problems,
including multi-way partition, balanced separator, and
maximum cut.",
acknowledgement = ack-nhfb,
}
@InProceedings{Williams:2013:NPV,
author = "Ryan Williams",
title = "Natural proofs versus derandomization",
crossref = "ACM:2013:SPF",
pages = "21--30",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488612",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study connections between Natural Proofs,
derandomization, and the problem of proving ``weak''
circuit lower bounds such as $ {\rm NEXP} \not \subset
{\rm TC}^0 $, which are still wide open. Natural Proofs
have three properties: they are constructive (an
efficient algorithm $A$ is embedded in them), have
largeness ($A$ accepts a large fraction of strings),
and are useful ($A$ rejects all strings which are truth
tables of small circuits). Strong circuit lower bounds
that are ``naturalizing'' would contradict present
cryptographic understanding, yet the vast majority of
known circuit lower bound proofs are naturalizing. So
it is imperative to understand how to pursue un-Natural
Proofs. Some heuristic arguments say constructivity
should be circumventable. Largeness is inherent in many
proof techniques, and it is probably our presently weak
techniques that yield constructivity. We prove:
Constructivity is unavoidable, even for NEXP lower
bounds. Informally, we prove for all ``typical''
non-uniform circuit classes $C$, $ {\rm NEXP} \not
\subset C $ if and only if there is a polynomial-time
algorithm distinguishing some function from all
functions computable by $C$-circuits. Hence $ {\rm
NEXP} \not \subset C $ is equivalent to exhibiting a
constructive property useful against $C$. There are no
P-natural properties useful against $C$ if and only if
randomized exponential time can be ``derandomized''
using truth tables of circuits from $C$ as random
seeds. Therefore the task of proving there are no
$P$-natural properties is inherently a derandomization
problem, weaker than but implied by the existence of
strong pseudorandom functions. These characterizations
are applied to yield several new results. The two main
applications are that $ {\rm NEXP} \cap {\rm coNEXP} $
does not have $ n^{\log n} $ size ACC circuits, and a
mild derandomization result for RP.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bei:2013:CTE,
author = "Xiaohui Bei and Ning Chen and Shengyu Zhang",
title = "On the complexity of trial and error",
crossref = "ACM:2013:SPF",
pages = "31--40",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488613",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Motivated by certain applications from physics,
biochemistry, economics, and computer science in which
the objects under investigation are unknown or not
directly accessible because of various limitations, we
propose a trial-and-error model to examine search
problems in which inputs are unknown. More
specifically, we consider constraint satisfaction
problems $ \wedge_i C_i $, where the constraints $ C_i
$ are hidden, and the goal is to find a solution
satisfying all constraints. We can adaptively propose a
candidate solution (i.e., trial), and there is a
verification oracle that either confirms that it is a
valid solution, or returns the index i of a violated
constraint (i.e., error), with the exact content of $
C_i $ still hidden. We studied the time and trial
complexities of a number of natural CSPs, summarized as
follows. On one hand, despite the seemingly very little
information provided by the oracle, efficient
algorithms do exist for Nash, Core, Stable Matching,
and SAT problems, whose unknown-input versions are
shown to be as hard as the corresponding known-input
versions up to a factor of polynomial. The techniques
employed vary considerably, including, e.g., order
theory and the ellipsoid method with a strong
separation oracle. On the other hand, there are
problems whose complexities are substantially increased
in the unknown-input model. In particular, no
time-efficient algorithms exist for Graph Isomorphism
and Group Isomorphism (unless PH collapses or P = NP).
The proofs use quite nonstandard reductions, in which
an efficient simulator is carefully designed to
simulate a desirable but computationally unaffordable
oracle. Our model investigates the value of input
information, and our results demonstrate that the lack
of input information can introduce various levels of
extra difficulty. The model accommodates a wide range
of combinatorial and algebraic structures, and exhibits
intimate connections with (and hopefully can also serve
as a useful supplement to) certain existing learning
and complexity theories.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bhawalkar:2013:COF,
author = "Kshipra Bhawalkar and Sreenivas Gollapudi and Kamesh
Munagala",
title = "Coevolutionary opinion formation games",
crossref = "ACM:2013:SPF",
pages = "41--50",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488615",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present game-theoretic models of opinion formation
in social networks where opinions themselves co-evolve
with friendships. In these models, nodes form their
opinions by maximizing agreements with friends weighted
by the strength of the relationships, which in turn
depend on difference in opinion with the respective
friends. We define a social cost of this process by
generalizing recent work of Bindel et al., FOCS 2011.
We tightly bound the price of anarchy of the resulting
dynamics via local smoothness arguments, and
characterize it as a function of how much nodes value
their own (intrinsic) opinion, as well as how strongly
they weigh links to friends with whom they agree
more.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chawla:2013:PIM,
author = "Shuchi Chawla and Jason D. Hartline and David Malec
and Balasubramanian Sivan",
title = "Prior-independent mechanisms for scheduling",
crossref = "ACM:2013:SPF",
pages = "51--60",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488616",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the makespan minimization problem with
unrelated selfish machines under the assumption that
job sizes are stochastic. We design simple truthful
mechanisms that under different distributional
assumptions provide constant and sublogarithmic
approximations to expected makespan. Our mechanisms are
prior-independent in that they do not rely on knowledge
of the job size distributions. Prior-independent
approximations were previously known only for the
revenue maximization objective [13, 11, 26]. In
contrast to our results, in prior-free settings no
truthful anonymous deterministic mechanism for the
makespan objective can provide a sublinear
approximation [3].",
acknowledgement = ack-nhfb,
}
@InProceedings{Feldman:2013:CWE,
author = "Michal Feldman and Nick Gravin and Brendan Lucier",
title = "Combinatorial {Walrasian Equilibrium}",
crossref = "ACM:2013:SPF",
pages = "61--70",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488617",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study a combinatorial market design problem, where
a collection of indivisible objects is to be priced and
sold to potential buyers subject to equilibrium
constraints. The classic solution concept for such
problems is Walrasian Equilibrium (WE), which provides
a simple and transparent pricing structure that
achieves optimal social welfare. The main weakness of
the WE notion is that it exists only in very
restrictive cases. To overcome this limitation, we
introduce the notion of a Combinatorial Walrasian
equilibium (CWE), a natural relaxation of WE. The
difference between a CWE and a (non-combinatorial) WE
is that the seller can package the items into
indivisible bundles prior to sale, and the market does
not necessarily clear. We show that every valuation
profile admits a CWE that obtains at least half of the
optimal (unconstrained) social welfare. Moreover, we
devise a poly-time algorithm that, given an arbitrary
allocation X, computes a CWE that achieves at least
half of the welfare of X. Thus, the economic problem of
finding a CWE with high social welfare reduces to the
algorithmic problem of social-welfare approximation. In
addition, we show that every valuation profile admits a
CWE that extracts a logarithmic fraction of the optimal
welfare as revenue. Finally, these results are
complemented by strong lower bounds when the seller is
restricted to using item prices only, which motivates
the use of bundles. The strength of our results derives
partly from their generality --- our results hold for
arbitrary valuations that may exhibit complex
combinations of substitutes and complements.",
acknowledgement = ack-nhfb,
}
@InProceedings{Naor:2013:ERN,
author = "Assaf Naor and Oded Regev and Thomas Vidick",
title = "Efficient rounding for the noncommutative
{Grothendieck} inequality",
crossref = "ACM:2013:SPF",
pages = "71--80",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488618",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The classical Grothendieck inequality has applications
to the design of approximation algorithms for NP-hard
optimization problems. We show that an algorithmic
interpretation may also be given for a noncommutative
generalization of the Grothendieck inequality due to
Pisier and Haagerup. Our main result, an efficient
rounding procedure for this inequality, leads to a
constant-factor polynomial time approximation algorithm
for an optimization problem which generalizes the Cut
Norm problem of Frieze and Kannan, and is shown here to
have additional applications to robust principle
component analysis and the orthogonal Procrustes
problem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Clarkson:2013:LRA,
author = "Kenneth L. Clarkson and David P. Woodruff",
title = "Low rank approximation and regression in input
sparsity time",
crossref = "ACM:2013:SPF",
pages = "81--90",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488620",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We design a new distribution over $ \poly (r
\epsilon^{-1}) \times n $ matrices $S$ so that for any
fixed $ n \times d $ matrix $A$ of rank $r$, with
probability at least $ 9 / 10 $, $ S A x_2 = (1 \pm
\epsilon) A x_2 $ simultaneously for all $ x \in R^d $.
Such a matrix $S$ is called a subspace embedding.
Furthermore, $ S A $ can be computed in $ O({\rm
nnz}(A)) + \tilde O (r^2 \epsilon^{-2}) $ time, where $
{\rm nnz}(A) $ is the number of non-zero entries of
$A$. This improves over all previous subspace
embeddings, which required at least $ \Omega (n d \log
d) $ time to achieve this property. We call our
matrices $S$ sparse embedding matrices. Using our
sparse embedding matrices, we obtain the fastest known
algorithms for overconstrained least-squares
regression, low-rank approximation, approximating all
leverage scores, and $ l_p $ -regression: to output an
$ x' $ for which $ A x' - b_2 \leq (1 + \epsilon)
\min_x A x - b_2 $ for an $ n \times d $ matrix $A$ and
an $ n \times 1 $ column vector $b$, we obtain an
algorithm running in $ O({\rm nnz}(A)) + \tilde O(d^3
\epsilon^{-2}) $ time, and another in $ O({\rm nnz}(A)
\log (1 / \epsilon)) + \tilde O(d^3 \log (1 /
\epsilon)) $ time. (Here $ \tilde O(f) = f \cdot l o
g^{O(1)} (f) $.) to obtain a decomposition of an $ n
\times n $ matrix $A$ into a product of an $ n \times k
$ matrix $L$, a $ k \times k $ diagonal matrix $D$, and
a $ n \times k $ matrix $W$, for which $ \{ F A - L D W
\} \leq (1 + \epsilon) F \{ A - A_k \} $, where $ A_k $
is the best rank-$k$ approximation, our algorithm runs
in $ O({\rm nnz}(A)) + \tilde O(n k^2 \epsilon^{-4}
\log n + k^3 \epsilon^{-5} \log^2 n) $ time. to output
an approximation to all leverage scores of an $ n
\times d $ input matrix $A$ simultaneously, with
constant relative error, our algorithms run in $ O({\rm
nnz}(A) \log n) + \tilde O(r^3) $ time. to output an $
x' $ for which $ A x' - b_p \leq (1 + \epsilon) \min_x
A x - b_p $ for an $ n \times d $ matrix $A$ and an $ n
\times 1 $ column vector $b$, we obtain an algorithm
running in $ O({\rm nnz}(A) \log n) + \poly (r
\epsilon^{-1}) $ time, for any constant $ 1 \leq p <
\infty $. We optimize the polynomial factors in the
above stated running times, and show various tradeoffs.
Finally, we provide preliminary experimental results
which suggest that our algorithms are of interest in
practice.",
acknowledgement = ack-nhfb,
}
@InProceedings{Meng:2013:LDS,
author = "Xiangrui Meng and Michael W. Mahoney",
title = "Low-distortion subspace embeddings in input-sparsity
time and applications to robust linear regression",
crossref = "ACM:2013:SPF",
pages = "91--100",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488621",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Low-distortion embeddings are critical building blocks
for developing random sampling and random projection
algorithms for common linear algebra problems. We show
that, given a matrix $ A \in R^{n x d} $ with $ n \gg d
$ and $ a p \in [1, 2) $, with a constant probability,
we can construct a low-distortion embedding matrix $
\Pi \in R^{O({\rm poly}(d)) x n} $ that embeds $ A_p $,
the $ l_p $ subspace spanned by $A$'s columns, into $
(R^{O({\rm poly}(d))}, | \cdot |_p) $; the distortion
of our embeddings is only $ O({\rm poly}(d)) $, and we
can compute $ \Pi A $ in $ O(n n z(A)) $ time, i.e.,
input-sparsity time. Our result generalizes the
input-sparsity time $ l_2 $ subspace embedding by
Clarkson and Woodruff [STOC'13]; and for completeness,
we present a simpler and improved analysis of their
construction for $ l_2 $. These input-sparsity time $
l_p $ embeddings are optimal, up to constants, in terms
of their running time; and the improved running time
propagates to applications such as $ (1 p m \epsilon)
$-distortion $ l_p $ subspace embedding and
relative-error $ l_p $ regression. For $ l_2 $, we show
that a $ (1 + \epsilon) $-approximate solution to the $
l_2 $ regression problem specified by the matrix $A$
and a vector $ b \in R^n $ can be computed in $ O(n n
z(A) + d^3 \log (d / \epsilon) / \epsilon^2) $ time;
and for $ l_p $, via a subspace-preserving sampling
procedure, we show that a $ (1 p m \epsilon)
$-distortion embedding of $ A_p $ into $ R^{O({\rm
poly}(d))} $ can be computed in $ O(n n z(A) \cdot \log
n) $ time, and we also show that a $ (1 + \epsilon)
$-approximate solution to the $ l_p $ regression
problem $ \min_{x \in R^d} |A x - b|_p $ can be
computed in $ O(n n z(A) \cdot \log n + {\rm poly}(d)
\log (1 / \epsilon) / \epsilon^2) $ time. Moreover, we
can also improve the embedding dimension or
equivalently the sample size to $ O(d^{3 + p / 2} \log
(1 / \epsilon) / \epsilon^2) $ without increasing the
complexity.",
acknowledgement = ack-nhfb,
}
@InProceedings{Nelson:2013:SLB,
author = "Jelani Nelson and Huy L. Nguyen",
title = "Sparsity lower bounds for dimensionality reducing
maps",
crossref = "ACM:2013:SPF",
pages = "101--110",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488622",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give near-tight lower bounds for the sparsity
required in several dimensionality reducing linear
maps. First, consider the Johnson--Lindenstrauss (JL)
lemma which states that for any set of $n$ vectors in $
R^d $ there is an $ A \in R^{m \times d} $ with $ m =
O(\epsilon^{-2} \log n) $ such that mapping by $A$
preserves the pairwise Euclidean distances up to a $ 1
\pm \epsilon $ factor. We show there exists a set of
$n$ vectors such that any such $A$ with at most $s$
non-zero entries per column must have $ s = \Omega
(\epsilon^{-1} \log n / \log (1 / \epsilon)) $ if $ m <
O(n / \log (1 / \epsilon)) $. This improves the lower
bound of $ \Omega (\min \{ \epsilon^{-2}, \epsilon^{-1}
\sqrt (\log_m d) \}) $ by [Dasgupta-Kumar-Sarlos, STOC
2010], which only held against the stronger property of
distributional JL, and only against a certain
restricted class of distributions. Meanwhile our lower
bound is against the JL lemma itself, with no
restrictions. Our lower bound matches the sparse JL
upper bound of [Kane-Nelson, SODA 2012] up to an $
O(\log (1 / \epsilon)) $ factor. Next, we show that any
$ m \times n $ matrix with the $k$-restricted isometry
property (RIP) with constant distortion must have $
\Omega (k \log (n / k)) $ non-zeroes per column if $ m
= O(k \log (n / k)) $, the optimal number of rows for
RIP, and $ k < n / \polylog n $. This improves the
previous lower bound of $ \Omega (\min \{ k, n / m \})
$ by [Chandar, 2010] and shows that for most $k$ it is
impossible to have a sparse RIP matrix with an optimal
number of rows. Both lower bounds above also offer a
tradeoff between sparsity and the number of rows.
Lastly, we show that any oblivious distribution over
subspace embedding matrices with 1 non-zero per column
and preserving distances in a $d$ dimensional-subspace
up to a constant factor must have at least $ \Omega
(d^2) $ rows. This matches an upper bound in
[Nelson-Nguy{\^e}n, arXiv abs/1211.1002] and shows the
impossibility of obtaining the best of both of
constructions in that work, namely 1 non-zero per
column and $ d \cdot \polylog d $ rows.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bitansky:2013:RCB,
author = "Nir Bitansky and Ran Canetti and Alessandro Chiesa and
Eran Tromer",
title = "Recursive composition and bootstrapping for {SNARKS}
and proof-carrying data",
crossref = "ACM:2013:SPF",
pages = "111--120",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488623",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Succinct non-interactive arguments of knowledge
(SNARKs) enable verifying NP statements with complexity
that is essentially independent of that required for
classical NP verification. In particular, they provide
strong solutions to the problem of verifiably
delegating computation. We construct the first
fully-succinct publicly-verifiable SNARK. To do that,
we first show how to ``bootstrap'' any SNARK that
requires expensive preprocessing to obtain a SNARK that
does not, while preserving public verifiability. We
then apply this transformation to known SNARKs with
preprocessing. Moreover, the SNARK we construct only
requires of the prover time and space that are
essentially the same as that required for classical NP
verification. Our transformation assumes only
collision-resistant hashing; curiously, it does not
rely on PCPs. We also show an analogous transformation
for privately-verifiable SNARKs, assuming
fully-homomorphic encryption. At the heart of our
transformations is a technique for recursive
composition of SNARKs. This technique uses in an
essential way the proof-carrying data (PCD) framework,
which extends SNARKs to the setting of distributed
networks of provers and verifiers. Concretely, to
bootstrap a given SNARK, we recursively compose the
SNARK to obtain a ``weak'' PCD system for shallow
distributed computations, and then use the PCD
framework to attain stronger notions of SNARKs and PCD
systems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hardt:2013:HRL,
author = "Moritz Hardt and David P. Woodruff",
title = "How robust are linear sketches to adaptive inputs?",
crossref = "ACM:2013:SPF",
pages = "121--130",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488624",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Linear sketches are powerful algorithmic tools that
turn an $n$-dimensional input into a concise
lower-dimensional representation via a linear
transformation. Such sketches have seen a wide range of
applications including norm estimation over data
streams, compressed sensing, and distributed computing.
In almost any realistic setting, however, a linear
sketch faces the possibility that its inputs are
correlated with previous evaluations of the sketch.
Known techniques no longer guarantee the correctness of
the output in the presence of such correlations. We
therefore ask: Are linear sketches inherently
non-robust to adaptively chosen inputs? We give a
strong affirmative answer to this question.
Specifically, we show that no linear sketch
approximates the Euclidean norm of its input to within
an arbitrary multiplicative approximation factor on a
polynomial number of adaptively chosen inputs. The
result remains true even if the dimension of the sketch
is d=n-o(n) and the sketch is given unbounded
computation time. Our result is based on an algorithm
with running time polynomial in d that adaptively finds
a distribution over inputs on which the sketch is
incorrect with constant probability. Our result implies
several corollaries for related problems including
l$_p$ -norm estimation and compressed sensing. Notably,
we resolve an open problem in compressed sensing
regarding the feasibility of l$_2$ /l$_2$ -recovery
guarantees in presence of computationally bounded
adversaries.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bohm:2013:EDO,
author = "Stanislav B{\"o}hm and Stefan G{\"o}ller and Petr
Jancar",
title = "Equivalence of deterministic one-counter automata is
{NL}-complete",
crossref = "ACM:2013:SPF",
pages = "131--140",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488626",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove that language equivalence of deterministic
one-counter automata is NL-complete. This improves the
superpolynomial time complexity upper bound shown by
Valiant and Paterson in 1975. Our main contribution is
to prove that two deterministic one-counter automata
are inequivalent if and only if they can be
distinguished by a word of length polynomial in the
size of the two input automata.",
acknowledgement = ack-nhfb,
}
@InProceedings{Burgisser:2013:ELB,
author = "Peter B{\"u}rgisser and Christian Ikenmeyer",
title = "Explicit lower bounds via geometric complexity
theory",
crossref = "ACM:2013:SPF",
pages = "141--150",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488627",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove the lower bound $ R (M_m) \geq 3 / 2 m^2 - 2
$ on the border rank of $ m \times m $ matrix
multiplication by exhibiting explicit representation
theoretic (occurrence) obstructions in the sense of
Mulmuley and Sohoni's geometric complexity theory (GCT)
program. While this bound is weaker than the one
recently obtained by Landsberg and Ottaviani, these are
the first significant lower bounds obtained within the
GCT program. Behind the proof is an explicit
description of the highest weight vectors in Sym$^d
\otimes^3 (C^n)*$ in terms of combinatorial objects,
called obstruction designs. This description results
from analyzing the process of polarization and
Schur--Weyl duality.",
acknowledgement = ack-nhfb,
}
@InProceedings{Braverman:2013:IEC,
author = "Mark Braverman and Ankit Garg and Denis Pankratov and
Omri Weinstein",
title = "From information to exact communication",
crossref = "ACM:2013:SPF",
pages = "151--160",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488628",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We develop a new local characterization of the
zero-error information complexity function for
two-party communication problems, and use it to compute
the exact internal and external information complexity
of the 2-bit AND function: $ {\rm IC}({\rm AND}, 0) =
C_{\wedge } \cong 1.4923 $ bits, and $ {\rm IC}^{ext}
({\rm AND}, 0) = \log_2 3 \cong 1.5839 $ bits. This
leads to a tight (upper and lower bound)
characterization of the communication complexity of the
set intersection problem on subsets of $ \{ 1, \ldots
{}, n \} $ (the player are required to compute the
intersection of their sets), whose randomized
communication complexity tends to $ C_{\wedge } \cdot n
\pm o(n) $ as the error tends to zero. The
information-optimal protocol we present has an infinite
number of rounds. We show this is necessary by proving
that the rate of convergence of the r-round information
cost of AND to $ {\rm IC}({\rm AND}, 0) = C_{\wedge } $
behaves like $ \Theta (1 / r^2) $, i.e. that the
$r$-round information complexity of AND is $ C_\wedge
+ \Theta (1 / r^2) $. We leverage the tight analysis
obtained for the information complexity of AND to
calculate and prove the exact communication complexity
of the set disjointness function $ {\rm Disj}_n (X, Y)
= - v_{i = 1}^n {\rm AND}(x_i, y_i) $ with error
tending to $0$, which turns out to be $ = C_{\rm DISJ}
\cdot n \pm o(n) $, where $ C_{\rm DISJ} \cong 0.4827
$. Our rate of convergence results imply that an
asymptotically optimal protocol for set disjointness
will have to use $ \omega (1) $ rounds of
communication, since every $r$-round protocol will be
sub-optimal by at least $ \Omega (n / r^2) $ bits of
communication. We also obtain the tight bound of $ 2 /
\ln 2 k \pm o(k) $ on the communication complexity of
disjointness of sets of size $ \leq k $. An asymptotic
bound of $ \Theta (k) $ was previously shown by Hastad
and Wigderson.",
acknowledgement = ack-nhfb,
}
@InProceedings{Braverman:2013:ICA,
author = "Mark Braverman and Ankur Moitra",
title = "An information complexity approach to extended
formulations",
crossref = "ACM:2013:SPF",
pages = "161--170",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488629",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove an unconditional lower bound that any linear
program that achieves an $ O(n^{1 - \epsilon }) $
approximation for clique has size $ 2^{ \Omega (n
\epsilon)} $. There has been considerable recent
interest in proving unconditional lower bounds against
any linear program. Fiorini et al. proved that there is
no polynomial sized linear program for traveling
salesman. Braun et al. proved that there is no
polynomial sized $ O(n^{1 / 2 - \epsilon })
$-approximate linear program for clique. Here we prove
an optimal and unconditional lower bound against linear
programs for clique that matches Hastad's celebrated
hardness result. Interestingly, the techniques used to
prove such lower bounds have closely followed the
progression of techniques used in communication
complexity. Here we develop an information theoretic
framework to approach these questions, and we use it to
prove our main result. Also we resolve a related
question: How many bits of communication are needed to
get $ \epsilon $ advantage over random guessing for
disjointness? Kalyanasundaram and Schnitger proved that
a protocol that gets constant advantage requires $
\Omega (n) $ bits of communication. This result in
conjunction with amplification implies that any
protocol that gets $ \epsilon $-advantage requires $
\Omega (\epsilon^2 n) $ bits of communication. Here we
improve this bound to $ \Omega (\epsilon n) $, which is
optimal for any $ \epsilon > 0 $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Komargodski:2013:ACL,
author = "Ilan Komargodski and Ran Raz",
title = "Average-case lower bounds for formula size",
crossref = "ACM:2013:SPF",
pages = "171--180",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488630",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give an explicit function $ h : \{ 0, 1 \}^n \to \{
0, 1 \} $ such that any deMorgan formula of size $
O(n^{2.499}) $ agrees with $h$ on at most $ 1 / 2 +
\epsilon $ fraction of the inputs, where $ \epsilon $
is exponentially small (i.e. $ \epsilon = 2^{-n \Omega
(1)} $ ). We also show, using the same technique, that
any boolean formula of size $ O(n^{1.999}) $ over the
complete basis, agrees with $h$ on at most $ 1 / 2 +
\epsilon $ fraction of the inputs, where $ \epsilon $
is exponentially small (i.e. $ \epsilon = 2^{-vn \Omega
(1)} $ ). Our construction is based on Andreev's $
\Omega (n^{2.5 - o(1)}) $ formula size lower bound that
was proved for the case of exact computation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2013:CNM,
author = "Xi Chen and Dimitris Paparas and Mihalis Yannakakis",
title = "The complexity of non-monotone markets",
crossref = "ACM:2013:SPF",
pages = "181--190",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488632",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We introduce the notion of non-monotone utilities,
which covers a wide variety of utility functions in
economic theory. We show that it is PPAD-hard to
compute an approximate Arrow--Debreu market equilibrium
in markets with linear and non-monotone utilities.
Building on this result, we settle the long-standing
open problem regarding the computation of an
approximate Arrow--Debreu market equilibrium in markets
with CES utilities, by proving that it is PPAD-complete
when the Constant Elasticity of Substitution parameter,
$ \rho $, is any constant less than $ - 1 $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cheung:2013:TBG,
author = "Yun Kuen Cheung and Richard Cole and Nikhil Devanur",
title = "Tatonnement beyond gross substitutes?: gradient
descent to the rescue",
crossref = "ACM:2013:SPF",
pages = "191--200",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488633",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Tatonnement is a simple and natural rule for updating
prices in Exchange (Arrow--Debreu) markets. In this
paper we define a class of markets for which
tatonnement is equivalent to gradient descent. This is
the class of markets for which there is a convex
potential function whose gradient is always equal to
the negative of the excess demand and we call it Convex
Potential Function (CPF) markets. We show the following
results. CPF markets contain the class of Eisenberg
Gale (EG) markets, defined previously by Jain and
Vazirani. The subclass of CPF markets for which the
demand is a differentiable function contains exactly
those markets whose demand function has a symmetric
negative semi-definite Jacobian. We define a family of
continuous versions of tatonnement based on gradient
descent using a Bregman divergence. As we show, all
processes in this family converge to an equilibrium for
any CPF market. This is analogous to the classic result
for markets satisfying the Weak Gross Substitutes
property. A discrete version of tatonnement converges
toward the equilibrium for the following markets of
complementary goods; its convergence rate for these
settings is analyzed using a common potential function.
Fisher markets in which all buyers have Leontief
utilities. The tatonnement process reduces the distance
to the equilibrium, as measured by the potential
function, to an $ \epsilon $ fraction of its initial
value in $ O(1 / \epsilon) $ rounds of price updates.
Fisher markets in which all buyers have complementary
CES utilities. Here, the distance to the equilibrium is
reduced to an $ \epsilon $ fraction of its initial
value in $ O(\log (1 / \epsilon)) $ rounds of price
updates. This shows that tatonnement converges for the
entire range of Fisher markets when buyers have
complementary CES utilities, in contrast to prior work,
which could analyze only the substitutes range,
together with a small portion of the complementary
range.",
acknowledgement = ack-nhfb,
}
@InProceedings{Feldman:2013:SAA,
author = "Michal Feldman and Hu Fu and Nick Gravin and Brendan
Lucier",
title = "Simultaneous auctions are (almost) efficient",
crossref = "ACM:2013:SPF",
pages = "201--210",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488634",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Simultaneous item auctions are simple and practical
procedures for allocating items to bidders with
potentially complex preferences. In a simultaneous
auction, every bidder submits independent bids on all
items simultaneously. The allocation and prices are
then resolved for each item separately, based solely on
the bids submitted on that item. We study the
efficiency of Bayes-Nash equilibrium (BNE) outcomes of
simultaneous first- and second-price auctions when
bidders have complement-free (a.k.a. subadditive)
valuations. While it is known that the social welfare
of every pure Nash equilibrium (NE) constitutes a
constant fraction of the optimal social welfare, a pure
NE rarely exists, and moreover, the full information
assumption is often unrealistic. Therefore, quantifying
the welfare loss in Bayes-Nash equilibria is of
particular interest. Previous work established a
logarithmic bound on the ratio between the social
welfare of a BNE and the expected optimal social
welfare in both first-price auctions (Hassidim et al.,
2011) and second-price auctions (Bhawalkar and
Roughgarden, 2011), leaving a large gap between a
constant and a logarithmic ratio. We introduce a new
proof technique and use it to resolve both of these
gaps in a unified way. Specifically, we show that the
expected social welfare of any BNE is at least 1/2 of
the optimal social welfare in the case of first-price
auctions, and at least 1/4 in the case of second-price
auctions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Syrgkanis:2013:CEM,
author = "Vasilis Syrgkanis and Eva Tardos",
title = "Composable and efficient mechanisms",
crossref = "ACM:2013:SPF",
pages = "211--220",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488635",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We initiate the study of efficient mechanism design
with guaranteed good properties even when players
participate in multiple mechanisms simultaneously or
sequentially. We define the class of smooth mechanisms,
related to smooth games defined by Roughgarden, that
can be thought of as mechanisms that generate
approximately market clearing prices. We show that
smooth mechanisms result in high quality outcome both
in equilibrium and in learning outcomes in the full
information setting, as well as in Bayesian equilibrium
with uncertainty about participants. Our main result is
to show that smooth mechanisms compose well: smoothness
locally at each mechanism implies global efficiency.
For mechanisms where good performance requires that
bidders do not bid above their value, we identify the
notion of a weakly smooth mechanism. Weakly smooth
mechanisms, such as the Vickrey auction, are
approximately efficient under the no-overbidding
assumption, and the weak smoothness property is also
maintained by composition. In most of the paper we
assume participants have quasi-linear valuations. We
also extend some of our results to settings where
participants have budget constraints.",
acknowledgement = ack-nhfb,
}
@InProceedings{Goyal:2013:NBB,
author = "Vipul Goyal",
title = "Non-black-box simulation in the fully concurrent
setting",
crossref = "ACM:2013:SPF",
pages = "221--230",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488637",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present a new zero-knowledge argument protocol by
relying on the non-black-box simulation technique of
Barak (FOCS'01). Similar to the protocol of Barak, ours
is public-coin, is based on the existence of
collision-resistant hash functions, and, is not based
on ``rewinding techniques'' but rather uses
non-black-box simulation. However in contrast to the
protocol of Barak, our protocol is secure even if there
are any unbounded (polynomial) number of concurrent
sessions. This gives us the first construction of
public-coin concurrent zero-knowledge. Prior to our
work, Pass, Tseng and Wikstrom (SIAM J. Comp. 2011) had
shown that using black-box simulation, getting a
construction for even public-coin parallel
zero-knowledge is impossible. A public-coin concurrent
zero-knowledge protocol directly implies the existence
of a concurrent resettably-sound zero-knowledge
protocol. This is an improvement over the corresponding
construction of Deng, Goyal and Sahai (FOCS'09) which
was based on stronger assumptions. Furthermore, this
also directly leads to an alternative (and arguable
cleaner) construction of a simultaneous resettable
zero-knowledge argument system. An important feature of
our protocol is the existence of a ``straight-line''
simulator. This gives a fundamentally different tool
for constructing concurrently secure computation
protocols (for functionalities even beyond
zero-knowledge). The round complexity of our protocol
is $ n^\epsilon $ (for any constant $ \epsilon > 0 $ ),
and, the simulator runs in strict polynomial time. The
main technique behind our construction is purely
combinatorial in nature.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chung:2013:NBB,
author = "Kai-Min Chung and Rafael Pass and Karn Seth",
title = "Non-black-box simulation from one-way functions and
applications to resettable security",
crossref = "ACM:2013:SPF",
pages = "231--240",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488638",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The simulation paradigm, introduced by Goldwasser,
Micali and Rackoff, is of fundamental importance to
modern cryptography. In a breakthrough work from 2001,
Barak (FOCS'01) introduced a novel non-black-box
simulation technique. This technique enabled the
construction of new cryptographic primitives, such as
resettably-sound zero-knowledge arguments, that cannot
be proven secure using just black-box simulation
techniques. The work of Barak and its follow-ups,
however, all require stronger cryptographic hardness
assumptions than the minimal assumption of one-way
functions. In this work, we show how to perform
non-black-box simulation assuming just the existence of
one-way functions. In particular, we demonstrate the
existence of a constant-round resettably-sound
zero-knowledge argument based only on the existence of
one-way functions. Using this technique, we determine
necessary and sufficient assumptions for several other
notions of resettable security of zero-knowledge
proofs. An additional benefit of our approach is that
it seemingly makes practical implementations of
non-black-box zero-knowledge viable.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bitansky:2013:IAO,
author = "Nir Bitansky and Omer Paneth",
title = "On the impossibility of approximate obfuscation and
applications to resettable cryptography",
crossref = "ACM:2013:SPF",
pages = "241--250",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488639",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The traditional notion of program obfuscation requires
that an obfuscation \char`{\~P}rog of a program Prog
computes the exact same function as Prog, but beyond
that, the code of \char`{\~P}rog should not leak any
information about Prog. This strong notion of virtual
black-box security was shown by Barak et al. (CRYPTO
2001) to be impossible to achieve, for certain
unobfuscatable function families. The same work raised
the question of approximate obfuscation, where the
obfuscated \char`{\~P}rog is only required to
approximate Prog; that is, \char`{\~P}rog only agrees
with Prog with high enough probability on some input
distribution. We show that, assuming trapdoor
permutations, there exist families of robust
unobfuscatable functions for which even approximate
obfuscation is impossible. Specifically, obfuscation is
impossible even if the obfuscated \char`{\~P}rog is
only required to agree with Prog with probability
slightly more than 1/2, on a uniformly sampled input
(below 1/2-agreement, the function obfuscated by
\char`{\~P}rog is not uniquely defined). Additionally,
assuming only one-way functions, we rule out
approximate obfuscation where \char`{\~P}rog may output
bot with probability close to $1$, but otherwise must
agree with Prog. We demonstrate the power of robust
unobfuscatable functions by exhibiting new implications
to resettable protocols. Concretely, we reduce the
assumptions required for resettably-sound
zero-knowledge to one-way functions, as well as reduce
round-complexity. We also present a new simplified
construction of a simultaneously-resettable
zero-knowledge protocol. Finally, we construct a
three-message simultaneously-resettable
witness-indistinguishable argument of knowledge (with a
non-black-box knowledge extractor). Our constructions
use a new non-black-box simulation technique that is
based on a special kind of ``resettable slots''. These
slots are useful for a non-black-box simulator, but not
for a resetting prover.",
acknowledgement = ack-nhfb,
}
@InProceedings{Miles:2013:SCG,
author = "Eric Miles and Emanuele Viola",
title = "Shielding circuits with groups",
crossref = "ACM:2013:SPF",
pages = "251--260",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488640",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We show how to efficiently compile any given circuit C
into a leakage-resistant circuit C' such that any
function on the wires of C' that leaks information
during a computation C'(x) yields advantage in
computing the product of |C'|$^{ \Omega (1)}$ elements
of the alternating group A$_u$. In combination with new
compression bounds for A$_u$ products, also obtained
here, C' withstands leakage from virtually any class of
functions against which average-case lower bounds are
known. This includes communication protocols, and A$
C^0 $ circuits augmented with few arbitrary symmetric
gates. If N$ C^1 $ ' T$ C^0 $ then the construction
resists T$ C^0 $ leakage as well. We also conjecture
that our construction resists N$ C^1 $ leakage. In
addition, we extend the construction to the multi-query
setting by relying on a simple secure hardware
component. We build on Barrington's theorem [JCSS '89]
and on the previous leakage-resistant constructions by
Ishai et al. [Crypto '03] and Faust et al. [Eurocrypt
'10]. Our construction exploits properties of A$_u$
beyond what is sufficient for Barrington's theorem.",
acknowledgement = ack-nhfb,
}
@InProceedings{Babai:2013:QTC,
author = "Laszlo Babai and John Wilmes",
title = "Quasipolynomial-time canonical form for {Steiner}
designs",
crossref = "ACM:2013:SPF",
pages = "261--270",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488642",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A Steiner 2-design is a finite geometry consisting of
a set of ``points'' together with a set of ``lines''
(subsets of points of uniform cardinality) such that
each pair of points belongs to exactly one line. In
this paper we analyse the individualization/refinement
heuristic and conclude that after individualizing $
O(\log n) $ points (assigning individual colors to
them), the refinement process gives each point an
individual color. The following consequences are
immediate: (a) isomorphism of Steiner 2-designs can be
tested in $ n^{O(\log n)} $ time, where $n$ is the
number of lines; (b) a canonical form of Steiner
2-designs can be computed within the same time bound;
(c) all isomorphisms between two Steiner 2-designs can
be listed within the same time bound; (d) the number of
automorphisms of a Steiner 2-design is at most
n$^{O(\log n)}$ (a fact of interest to finite geometry
and group theory.) The best previous bound in each of
these four statements was moderately exponential, $
\exp (\tilde O(n^{1 / 4})) $ (Spielman, STOC'96). Our
result removes an exponential bottleneck from
Spielman's analysis of the Graph Isomorphism problem
for strongly regular graphs. The results extend to
Steiner $t$-designs for all $ t \geq 2 $. Strongly
regular (s.r.) graphs have been known as hard cases for
graph isomorphism testing; the best previously known
bound for this case is moderately exponential, $ \exp
(\tilde O(n^{1 / 3})) $ where $n$ is the number of
vertices (Spielman, STOC'96). Line graphs of Steiner
$2$-designs enter as a critical subclass via Neumaier's
1979 classification of s.r. graphs. Previously, $
n^{O(\log n)} $ isomorphism testing and canonical forms
for Steiner 2-designs was known for the case when the
lines of the Steiner 2-design have bounded length
(Babai and Luks, STOC'83). That paper relied on Luks's
group-theoretic divide-and-conquer algorithms and did
not yield a subexponential bound on the number of
automorphisms. To analyse the
individualization/refinement heuristic, we develop a
new structure theory of Steiner 2-designs based on the
analysis of controlled growth and on an addressing
scheme that produces a hierarchy of increasing sets of
pairwise independent, uniformly distributed points.
This scheme represents a new expression of the
structural homogeneity of Steiner 2-designs that allows
applications of the second moment method. We also
address the problem of reconstruction of Steiner
2-designs from their line-graphs beyond the point of
unique reconstructability, in a manner analogous to
list-decoding, and as a consequence achieve an $ \exp
(\tilde O(n^{1 / 6})) $ bound for isomorphism testing
for this class of s.r. graphs. Results, essentially
identical to our main results, were obtained
simultaneously by Xi Chen, Xiaorui Sun, and Shang-Hua
Teng, building on a different philosophy and
combinatorial structure theory than the present paper.
They do not claim an analysis of the
individualization/refinement algorithm but of a more
complex combinatorial algorithm. We comment on how this
paper fits into the overall project of improved
isomorphism testing for strongly regular graphs (the
ultimate goal being subexponential $ \exp (n^{o(1)}) $
time). In the remaining cases we need to deal with s.r.
graphs satisfying ``Neumaier's claw bound,'' permitting
the use of a separate set of asymptotic structural
tools. In joint work (in progress) with Chen, Sun, and
Teng, we address that case and have already pushed the
overall bound below $ \exp (\tilde O(n^{1 / 4})) $ The
present paper is a methodologically distinct and
stand-alone part of the overall project.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chen:2013:MSD,
author = "Xi Chen and Xiaorui Sun and Shang-Hua Teng",
title = "Multi-stage design for quasipolynomial-time
isomorphism testing of {Steiner} $2$-systems",
crossref = "ACM:2013:SPF",
pages = "271--280",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488643",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A standard heuristic for testing graph isomorphism is
to first assign distinct labels to a small set of
vertices of an input graph, and then propagate to
create new vertex labels across the graph, aiming to
assign distinct and isomorphism-invariant labels to all
vertices in the graph. This is usually referred to as
the individualization/refinement method for canonical
labeling of graphs. We present a quasipolynomial-time
algorithm for isomorphism testing of Steiner 2-systems.
A Steiner 2-system consists of points and lines, where
each line passes the same number of points and each
pair of points uniquely determines a line. Each Steiner
2-system induces a Steiner graph, in which vertices
represent lines and edges represent intersections of
lines. Steiner graphs are an important subfamily of
strongly regular graphs whose isomorphism testing has
challenged researchers for years. Inspired by both the
individualization/refinement method and the previous
analyses of Babai and Spielman, we consider an extended
framework for isomorphism testing of Steiner 2-systems,
in which we use a small set of randomly chosen points
and lines to build isomorphism-invariant multi-stage
combinatorial structures that are sufficient to
distinguish all pairs of points of a Steiner 2-system.
Applying this framework, we show that isomorphism of
Steiner 2-systems with $n$ lines can be tested in time
$\smash n^{O(\log n)}$, improving the previous best
bound of $ \smash \exp (\tilde O(n^{1 / 4})) $ by
Spielman. Before our result, quasipolynomial-time
isomorphism testing was only known for the case when
the line size is polylogarithmic, as shown by Babai and
Luks. A result essentially identical to ours was
obtained simultaneously by Laszlo Babai and John
Wilmes. They performed a direct analysis of the
individualization/refinement method, building on a
different philosophy and combinatorial structure
theory. We comment on how this paper fits into the
overall project of improved isomorphism testing for
strongly regular graphs (the ultimate goal being
subexponential $ \exp (n^{o(1)}) $ time). In the
remaining cases, we only need to deal with strongly
regular graphs satisfying ``Neumaier's claw bound,''
permitting the use of a separate set of asymptotic
structural tools. In joint work (in progress) with
Babai and Wilmes, we address that case and have already
pushed the overall bound below $ \smash \exp (\tilde
O(n^{1 / 4})) $. The present paper is a
methodologically distinct and stand-alone part of the
overall project.",
acknowledgement = ack-nhfb,
}
@InProceedings{Gupta:2013:SCB,
author = "Anupam Gupta and Kunal Talwar and David Witmer",
title = "Sparsest cut on bounded treewidth graphs: algorithms
and hardness results",
crossref = "ACM:2013:SPF",
pages = "281--290",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488644",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give a 2-approximation algorithm for the
non-uniform Sparsest Cut problem that runs in time $
n^{O(k)} $, where $k$ is the treewidth of the graph.
This improves on the previous $ 2^{2 k} $ approximation
in time $ \poly (n) 2^{O(k)} $ due to Chlamtac et al.
[18]. To complement this algorithm, we show the
following hardness results: If the non-uniform Sparsest
Cut has a $ \rho $-approximation for series-parallel
graphs (where $ \rho \geq 1 $ ), then the MaxCut
problem has an algorithm with approximation factor
arbitrarily close to $ 1 / \rho $. Hence, even for such
restricted graphs (which have treewidth 2), the
Sparsest Cut problem is NP-hard to approximate better
than $ 17 / 16 - \epsilon $ for $ \epsilon > 0 $;
assuming the Unique Games Conjecture the hardness
becomes $ 1 / \alpha_{GW} - \epsilon $. For graphs with
large (but constant) treewidth, we show a hardness
result of $ 2 - \epsilon $ assuming the Unique Games
Conjecture. Our algorithm rounds a linear program based
on (a subset of) the Sherali--Adams lift of the
standard Sparsest Cut LP. We show that even for
treewidth-2 graphs, the LP has an integrality gap close
to 2 even after polynomially many rounds of
Sherali--Adams. Hence our approach cannot be improved
even on such restricted graphs without using a stronger
relaxation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chekuri:2013:LTG,
author = "Chandra Chekuri and Julia Chuzhoy",
title = "Large-treewidth graph decompositions and
applications",
crossref = "ACM:2013:SPF",
pages = "291--300",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488645",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Treewidth is a graph parameter that plays a
fundamental role in several structural and algorithmic
results. We study the problem of decomposing a given
graph $G$ into node-disjoint subgraphs, where each
subgraph has sufficiently large treewidth. We prove two
theorems on the tradeoff between the number of the
desired subgraphs h, and the desired lower bound r on
the treewidth of each subgraph. The theorems assert
that, given a graph $G$ with treewidth $k$, a
decomposition with parameters $ h, r $ is feasible
whenever $ h r^2 \leq k / \polylog (k) $, or $ h^3 r
\leq k / \polylog (k) $ holds. We then show a framework
for using these theorems to bypass the well-known
Grid-Minor Theorem of Robertson and Seymour in some
applications. In particular, this leads to
substantially improved parameters in some
Erd{\H{o}}s--Posa-type results, and faster algorithms
for some fixed-parameter tractable problems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cygan:2013:FHC,
author = "Marek Cygan and Stefan Kratsch and Jesper Nederlof",
title = "Fast {Hamiltonicity} checking via bases of perfect
matchings",
crossref = "ACM:2013:SPF",
pages = "301--310",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488646",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "For an even integer $ t \geq 2 $, the Matching
Connectivity matrix $ H_t $ is a matrix that has rows
and columns both labeled by all perfect matchings of
the complete graph $ K_t $ on $t$ vertices; an entry $
H_t [M_1, M_2] $ is $1$ if $ M_1 \cup M_2 $ is a
Hamiltonian cycle and $0$ otherwise. Motivated by the
computational study of the Hamiltonicity problem, we
present three results on the structure of $ H_t $: We
first show that $ H_t $ has rank exactly $ 2^{t / 2 -
1} $ over GF(2) via an appropriate factorization that
explicitly provides families of matchings $ X_t $
forming bases for $ H_t $. Second, we show how to
quickly change representation between such bases.
Third, we notice that the sets of matchings $ X_t $
induce permutation matrices within $ H_t $. We use the
factorization to derive an $ 1.888^n n^{O(1)} $ time
Monte Carlo algorithm that solves the Hamiltonicity
problem in directed bipartite graphs. Our algorithm as
well counts the number of Hamiltonian cycles modulo two
in directed bipartite or undirected graphs in the same
time bound. Moreover, we use the fast basis change
algorithm from the second result to present a Monte
Carlo algorithm that given an undirected graph on $n$
vertices along with a path decomposition of width at
most pw decides Hamiltonicity in $ (2 + \sqrt 2)^{pw}
n^{O(1)} $ time. Finally, we use the third result to
show that for every $ \epsilon > 0 $ this cannot be
improved to $ (2 + \sqrt 2 - \epsilon)^{pw} n^{O(1)} $
time unless the Strong Exponential Time Hypothesis
fails, i.e., a faster algorithm for this problem would
imply the breakthrough result of an $ O((2 - \epsilon
')^n) $ time algorithm for CNF-Sat.",
acknowledgement = ack-nhfb,
}
@InProceedings{Keevash:2013:PTP,
author = "Peter Keevash and Fiachra Knox and Richard Mycroft",
title = "Polynomial-time perfect matchings in dense
hypergraphs",
crossref = "ACM:2013:SPF",
pages = "311--320",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488647",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Let H be a $k$-graph on $n$ vertices, with minimum
codegree at least n/k + cn for some fixed c > 0. In
this paper we construct a polynomial-time algorithm
which finds either a perfect matching in H or a
certificate that none exists. This essentially solves a
problem of Karpinski, Rucinski and Szymanska, who
previously showed that this problem is NP-hard for a
minimum codegree of n/k --- cn. Our algorithm relies on
a theoretical result of independent interest, in which
we characterise any such hypergraph with no perfect
matching using a family of lattice-based
constructions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Agrawal:2013:QPH,
author = "Manindra Agrawal and Chandan Saha and Nitin Saxena",
title = "Quasi-polynomial hitting-set for set-depth-{$ \Delta
$} formulas",
crossref = "ACM:2013:SPF",
pages = "321--330",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488649",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We call a depth-4 formula $C$ set-depth-4 if there
exists a (unknown) partition $ X_1 \sqcup \cdots \sqcup
X_d $ of the variable indices $ [n] $ that the top
product layer respects, i.e. $ C({{\rm term} x}) =
\Sigma_{i = 1}^k \prod_{j = 1}^d f_{i, j} ({{\rm term}
x}_{X j}) $, where $ f_{i, j} $ is a sparse polynomial
in $ F[{{\rm term} x}_{X j}] $. Extending this
definition to any depth --- we call a depth-$D$ formula
$C$ (consisting of alternating layers of $ \Sigma $ and
$ \Pi $ gates, with a $ \Sigma $-gate on top) a
set-depth-$D$ formula if every $ \Pi $-layer in $C$
respects a (unknown) partition on the variables; if $D$
is even then the product gates of the bottom-most $ \Pi
$-layer are allowed to compute arbitrary monomials. In
this work, we give a hitting-set generator for
set-depth-$D$ formulas (over any field) with running
time polynomial in $ \exp ((D^2 \log s)^{\Delta - 1})
$, where $s$ is the size bound on the input
set-depth-$D$ formula. In other words, we give a
quasi-polynomial time blackbox polynomial identity test
for such constant-depth formulas. Previously, the very
special case of $ D = 3 $ (also known as
set-multilinear depth-3 circuits) had no known
sub-exponential time hitting-set generator. This was
declared as an open problem by Shpilka {\&} Yehudayoff
(FnT-TCS 2010); the model being first studied by Nisan
{\&} Wigderson (FOCS 1995) and recently by Forbes {\&}
Shpilka (STOC 2012 {\&} ECCC TR12-115). Our work
settles this question, not only for depth-3 but, up to
depth $ \epsilon \log s / \log \log s $, for a fixed
constant $ \epsilon < 1 $. The technique is to
investigate depth-$D$ formulas via depth-$ (D - 1) $
formulas over a Hadamard algebra, after applying a
shift' on the variables. We propose a new algebraic
conjecture about the low-support rank-concentration in
the latter formulas, and manage to prove it in the case
of set-depth-$D$ formulas.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hardt:2013:BWC,
author = "Moritz Hardt and Aaron Roth",
title = "Beyond worst-case analysis in private singular vector
computation",
crossref = "ACM:2013:SPF",
pages = "331--340",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488650",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider differentially private approximate
singular vector computation. Known worst-case lower
bounds show that the error of any differentially
private algorithm must scale polynomially with the
dimension of the singular vector. We are able to
replace this dependence on the dimension by a natural
parameter known as the coherence of the matrix that is
often observed to be significantly smaller than the
dimension both theoretically and empirically. We also
prove a matching lower bound showing that our guarantee
is nearly optimal for every setting of the coherence
parameter. Notably, we achieve our bounds by giving a
robust analysis of the well-known power iteration
algorithm, which may be of independent interest. Our
algorithm also leads to improvements in worst-case
settings and to better low-rank approximations in the
spectral norm.",
acknowledgement = ack-nhfb,
}
@InProceedings{Hsu:2013:DPA,
author = "Justin Hsu and Aaron Roth and Jonathan Ullman",
title = "Differential privacy for the analyst via private
equilibrium computation",
crossref = "ACM:2013:SPF",
pages = "341--350",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488651",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give new mechanisms for answering exponentially
many queries from multiple analysts on a private
database, while protecting dif- ferential privacy both
for the individuals in the database and for the
analysts. That is, our mechanism's answer to each query
is nearly insensitive to changes in the queries asked
by other analysts. Our mechanism is the first to offer
differential privacy on the joint distribution over
analysts' answers, providing privacy for data an-
alysts even if the other data analysts collude or
register multiple accounts. In some settings, we are
able to achieve nearly optimal error rates (even
compared to mechanisms which do not offer an- alyst
privacy), and we are able to extend our techniques to
handle non-linear queries. Our analysis is based on a
novel view of the private query-release problem as a
two-player zero-sum game, which may be of independent
interest.",
acknowledgement = ack-nhfb,
}
@InProceedings{Nikolov:2013:GDP,
author = "Aleksandar Nikolov and Kunal Talwar and Li Zhang",
title = "The geometry of differential privacy: the sparse and
approximate cases",
crossref = "ACM:2013:SPF",
pages = "351--360",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488652",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study trade-offs between accuracy and privacy in
the context of linear queries over histograms. This is
a rich class of queries that includes contingency
tables and range queries and has been the focus of a
long line of work. For a given set of $d$ linear
queries over a database $ x \in R^N $, we seek to find
the differentially private mechanism that has the
minimum mean squared error. For pure differential
privacy, [5, 32] give an $ O(\log^2 d) $ approximation
to the optimal mechanism. Our first contribution is to
give an efficient $ O(\log^2 d) $ approximation
guarantee for the case of $ (\epsilon, \delta)
$-differential privacy. Our mechanism adds carefully
chosen correlated Gaussian noise to the answers. We
prove its approximation guarantee relative to the
hereditary discrepancy lower bound of [44], using tools
from convex geometry. We next consider the sparse case
when the number of queries exceeds the number of
individuals in the database, i.e. when $ d > n \Delta
|x|_1 $. The lower bounds used in the previous
approximation algorithm no longer apply --- in fact
better mechanisms are known in this setting [7, 27, 28,
31, 49]. Our second main contribution is to give an
efficient $ (\epsilon, \delta) $-differentially private
mechanism that, for any given query set $A$ and an
upper bound $n$ on $ |x|_1 $, has mean squared error
within $ \polylog (d, N) $ of the optimal for $A$ and
$n$. This approximation is achieved by coupling the
Gaussian noise addition approach with linear regression
over the $ l_1 $ ball. Additionally, we show a similar
polylogarithmic approximation guarantee for the optimal
$ \epsilon $-differentially private mechanism in this
sparse setting. Our work also shows that for arbitrary
counting queries, i.e. $A$ with entries in $ \{ 0, 1 \}
$, there is an $ \epsilon $-differentially private
mechanism with expected error $ \tilde O(\sqrt n) $ per
query, improving on the $ \tilde O(n^{2 / 3}) $ bound
of [7] and matching the lower bound implied by [15] up
to logarithmic factors. The connection between the
hereditary discrepancy and the privacy mechanism
enables us to derive the first polylogarithmic
approximation to the hereditary discrepancy of a matrix
$A$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ullman:2013:ACQ,
author = "Jonathan Ullman",
title = "Answering $ n_{2 + o(1)} $ counting queries with
differential privacy is hard",
crossref = "ACM:2013:SPF",
pages = "361--370",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488653",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A central problem in differentially private data
analysis is how to design efficient algorithms capable
of answering large numbers of counting queries on a
sensitive database. Counting queries are of the form
``What fraction of individual records in the database
satisfy the property $q$ ?'' We prove that if one-way
functions exist, then there is no algorithm that takes
as input a database $ {\rm db} \in {\rm dbset} $, and $
k = \tilde \Theta (n^2) $ arbitrary efficiently
computable counting queries, runs in time $ \poly (d,
n) $, and returns an approximate answer to each query,
while satisfying differential privacy. We also consider
the complexity of answering ``simple'' counting
queries, and make some progress in this direction by
showing that the above result holds even when we
require that the queries are computable by
constant-depth ($ {\rm AC}^0 $) circuits. Our result
is almost tight because it is known that $ \tilde
\Omega (n^2) $ counting queries can be answered
efficiently while satisfying differential privacy.
Moreover, many more than $ n^2 $ queries (even
exponential in $n$) can be answered in exponential
time. We prove our results by extending the connection
between differentially private query release and
cryptographic traitor-tracing schemes to the setting
where the queries are given to the sanitizer as input,
and by constructing a traitor-tracing scheme that is
secure in this setting.",
acknowledgement = ack-nhfb,
}
@InProceedings{Thorup:2013:BPS,
author = "Mikkel Thorup",
title = "Bottom-$k$ and priority sampling, set similarity and
subset sums with minimal independence",
crossref = "ACM:2013:SPF",
pages = "371--380",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488655",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider bottom-$k$ sampling for a set X, picking a
sample S$_k$ (X) consisting of the k elements that are
smallest according to a given hash function h. With
this sample we can estimate the relative size f=|Y|/|X|
of any subset Y as |S$_k$ (X) intersect Y|/k. A
standard application is the estimation of the Jaccard
similarity f=|A intersect B|/|A union B| between sets A
and B. Given the bottom-$k$ samples from A and B, we
construct the bottom-$k$ sample of their union as S$_k$
(A union B)=S$_k$ (S$_k$ (A) union S$_k$ (B)), and then
the similarity is estimated as |S$_k$ (A union B)
intersect S$_k$ (A) intersect S$_k$ (B)|/k. We show
here that even if the hash function is only
2-independent, the expected relative error is $ O(1
\sqrt (f_k)) $. For $ f_k = \Omega(1) $ this is
within a constant factor of the expected relative error
with truly random hashing. For comparison, consider the
classic approach of kxmin-wise where we use $k$ hash
independent functions $ h_1, \ldots {}, h_k $, storing
the smallest element with each hash function. For
kxmin-wise there is an at least constant bias with
constant independence, and it is not reduced with
larger $k$. Recently Feigenblat et al. showed that
bottom-$k$ circumvents the bias if the hash function is
8-independent and $k$ is sufficiently large. We get
down to 2-independence for any $k$. Our result is based
on a simply union bound, transferring generic
concentration bounds for the hashing scheme to the
bottom-$k$ sample, e.g., getting stronger probability
error bounds with higher independence. For weighted
sets, we consider priority sampling which adapts
efficiently to the concrete input weights, e.g.,
benefiting strongly from heavy-tailed input. This time,
the analysis is much more involved, but again we show
that generic concentration bounds can be applied.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lenzen:2013:FRT,
author = "Christoph Lenzen and Boaz Patt-Shamir",
title = "Fast routing table construction using small messages:
extended abstract",
crossref = "ACM:2013:SPF",
pages = "381--390",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488656",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We describe a distributed randomized algorithm to
construct routing tables. Given $ 0 < \epsilon \leq 1 /
2 $, the algorithm runs in time $ \tilde O(n^{1 / 2 +
\epsilon } + {\rm HD}) $, where $n$ is the number of
nodes and HD denotes the diameter of the network in
hops (i.e., as if the network is unweighted). The
weighted length of the produced routes is at most $
O(\epsilon^{-1} \log \epsilon^{-1}) $ times the optimal
weighted length. This is the first algorithm to break
the $ \Omega (n) $ complexity barrier for computing
weighted shortest paths even for a single source.
Moreover, the algorithm nearly meets the $ \tilde
\Omega (n^{1 / 2} + {\rm HD}) $ lower bound for
distributed computation of routing tables and
approximate distances (with optimality, up to $
\polylog $ factors, for $ \epsilon = 1 / \log n $).
The presented techniques have many applications,
including improved distributed approximation algorithms
for Generalized Steiner Forest, all-pairs distance
estimation, and estimation of the weighted diameter.",
acknowledgement = ack-nhfb,
}
@InProceedings{Mendes:2013:MAA,
author = "Hammurabi Mendes and Maurice Herlihy",
title = "Multidimensional approximate agreement in {Byzantine}
asynchronous systems",
crossref = "ACM:2013:SPF",
pages = "391--400",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488657",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The problem of $ \epsilon $-approximate agreement in
Byzantine asynchronous systems is well-understood when
all values lie on the real line. In this paper, we
generalize the problem to consider values that lie in $
R^m $, for $ m \geq 1 $, and present an optimal
protocol in regard to fault tolerance. Our scenario is
the following. Processes start with values in $ R^m $,
for $ m \geq 1 $, and communicate via message-passing.
The system is asynchronous: there is no upper bound on
processes' relative speeds or on message delay. Some
faulty processes can display arbitrarily malicious
(i.e. Byzantine) behavior. Non-faulty processes must
decide on values that are: (1) in $ R^m $; (2) within
distance $ \epsilon $ of each other; and (3) in the
convex hull of the non-faulty processes' inputs. We
give an algorithm with a matching lower bound on fault
tolerance: we require $ n > t(m + 2) $, where $n$ is
the number of processes, $t$ is the number of Byzantine
processes, and input and output values reside in $ R^m
$. Non-faulty processes send $ O(n^2 d \log (m /
\epsilon \max \{ \delta (d) : 1 \leq d \leq m \})) $
messages in total, where $ \delta (d) $ is the range of
non-faulty inputs projected at coordinate $d$. The
Byzantine processes do not affect the algorithm's
running time.",
acknowledgement = ack-nhfb,
}
@InProceedings{King:2013:BAP,
author = "Valerie King and Jared Saia",
title = "{Byzantine} agreement in polynomial expected time:
[extended abstract]",
crossref = "ACM:2013:SPF",
pages = "401--410",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488658",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In the classic asynchronous Byzantine agreement
problem, communication is via asynchronous
message-passing and the adversary is adaptive with full
information. In particular, the adversary can
adaptively determine which processors to corrupt and
what strategy these processors should use as the
algorithm proceeds; the scheduling of the delivery of
messages is set by the adversary, so that the delays
are unpredictable to the algorithm; and the adversary
knows the states of all processors at any time, and is
assumed to be computationally unbounded. Such an
adversary is also known as ``strong''. We present a
polynomial expected time algorithm to solve
asynchronous Byzantine Agreement with a strong
adversary that controls up to a constant fraction of
the processors. This is the first improvement in
running time for this problem since Ben-Or's
exponential expected time solution in 1983. Our
algorithm tolerates an adversary that controls up to a
$ 1 / 500 $ fraction of the processors.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chakrabarty:2013:MTB,
author = "Deeparnab Chakrabarty and C. Seshadhri",
title = "A $ o(n) $ monotonicity tester for {Boolean} functions
over the hypercube",
crossref = "ACM:2013:SPF",
pages = "411--418",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488660",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Given oracle access to a Boolean function $ f : \{ 0,
1 \}^n \to \{ 0, 1 \} $, we design a randomized tester
that takes as input a parameter $ \epsilon > 0 $, and
outputs Yes if the function is monotonically
non-increasing, and outputs No with probability $ > 2 /
3 $, if the function is $ \epsilon $-far from being
monotone, that is, $f$ needs to be modified at $
\epsilon $-fraction of the points to make it monotone.
Our non-adaptive, one-sided tester makes $ \tilde
O(n^{5 / 6} \epsilon^{-5 / 3}) $ queries to the
oracle.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chakrabarty:2013:OBM,
author = "Deeparnab Chakrabarty and C. Seshadhri",
title = "Optimal bounds for monotonicity and {Lipschitz}
testing over hypercubes and hypergrids",
crossref = "ACM:2013:SPF",
pages = "419--428",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488661",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The problem of monotonicity testing over the hypergrid
and its special case, the hypercube, is a classic
question in property testing. We are given query access
to $ f : [k]^n \to R $ (for some ordered range $R$).
The hypergrid/cube has a natural partial order given by
coordinate-wise ordering, denoted by prec. A function
is monotone if for all pairs $ x \prec y $, $ f(x) \leq
f(y) $. The distance to monotonicity, $ \epsilon_f $,
is the minimum fraction of values of $f$ that need to
be changed to make f monotone. For $ k = 2 $ (the
boolean hypercube), the usual tester is the edge
tester, which checks monotonicity on adjacent pairs of
domain points. It is known that the edge tester using $
O(\epsilon^{-1} n \log |R|) $ samples can distinguish a
monotone function from one where $ \epsilon_f >
\epsilon $. On the other hand, the best lower bound for
monotonicity testing over general $R$ is $ \Omega (n)
$. We resolve this long standing open problem and prove
that $ O(n / \epsilon) $ samples suffice for the edge
tester. For hypergrids, known testers require $
O(\epsilon^{-1} n \log k \log |R|) $ samples, while the
best known (non-adaptive) lower bound is $ \Omega
(\epsilon^{-1} n \log k) $. We give a (non-adaptive)
monotonicity tester for hypergrids running in $
O(\epsilon^{{-1} n \log k}) $ time. Our techniques lead
to optimal property testers (with the same running
time) for the natural Lipschitz property on hypercubes
and hypergrids. (A $c$-Lipschitz function is one where
$ |f(x) - f(y)| \leq c || x - y ||_1 $.) In fact, we
give a general unified proof for $ O(\epsilon^{-1} n
\log k) $-query testers for a class of
``bounded-derivative'' properties, a class containing
both monotonicity and Lipschitz.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bhattacharyya:2013:ELC,
author = "Arnab Bhattacharyya and Eldar Fischer and Hamed Hatami
and Pooya Hatami and Shachar Lovett",
title = "Every locally characterized affine-invariant property
is testable",
crossref = "ACM:2013:SPF",
pages = "429--436",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488662",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Set $ F = F_p $ for any fixed prime $ p \geq 2 $. An
affine-invariant property is a property of functions
over $ F^n $ that is closed under taking affine
transformations of the domain. We prove that all
affine-invariant properties having local
characterizations are testable. In fact, we show a
proximity-oblivious test for any such property cP,
meaning that given an input function $f$, we make a
constant number of queries to $f$, always accept if $f$
satisfies cP, and otherwise reject with probability
larger than a positive number that depends only on the
distance between $f$ and cP. More generally, we show
that any affine-invariant property that is closed under
taking restrictions to subspaces and has bounded
complexity is testable. We also prove that any property
that can be described as the property of decomposing
into a known structure of low-degree polynomials is
locally characterized and is, hence, testable. For
example, whether a function is a product of two
degree-$d$ polynomials, whether a function splits into
a product of d linear polynomials, and whether a
function has low rank are all examples of
degree-structural properties and are therefore locally
characterized. Our results depend on a new Gowers
inverse theorem by Tao and Ziegler for low
characteristic fields that decomposes any polynomial
with large Gowers norm into a function of a small
number of low-degree non-classical polynomials. We
establish a new equidistribution result for high rank
non-classical polynomials that drives the proofs of
both the testability results and the local
characterization of degree-structural properties.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kawarabayashi:2013:TSF,
author = "Ken-ichi Kawarabayashi and Yuichi Yoshida",
title = "Testing subdivision-freeness: property testing meets
structural graph theory",
crossref = "ACM:2013:SPF",
pages = "437--446",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488663",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Testing a property $P$ of graphs in the bounded-degree
model deals with the following problem: given a graph
$G$ of bounded degree $d$, we should distinguish (with
probability 2/3, say) between the case that $G$
satisfies P and the case that one should add/remove at
least $ \epsilon d n $ edges of $G$ to make it satisfy
$P$. In sharp contrast to property testing of dense
graphs, which is relatively well understood, only few
properties are known to be testable with a constant
number of queries in the bounded-degree model. In
particular, no global monotone (i.e., closed under edge
deletions) property that expander graphs can satisfy
has been shown to be testable in constant time so far.
In this paper, we identify for the first time a natural
family of global monotone property that expander graphs
can satisfy and can be efficiently tested in the
bounded degree model. Specifically, we show that, for
any integer $ t \geq 1 $, $ K_t $-subdivision-freeness
is testable with a constant number of queries in the
bounded-degree model. This property was not previously
known to be testable even with o(n) queries. Note that
an expander graph with all degree less than $ t - 1 $
does not have a $ K_t $-subdivision. The proof is based
on a novel combination of some results that develop the
framework of partitioning oracles, together with
structural graph theory results that develop the
seminal graph minor theory by Robertson and Seymour. As
far as we aware, this is the first result that bridges
property testing and structural graph theory. Although
we know a rough structure for graphs without $H$-minors
from the famous graph minor theory by Robertson and
Seymour, there is no corresponding structure theorem
for graphs without $H$-subdivisions so far, even $ K_5
$-subdivision-free graphs. Therefore, subdivisions and
minors are very different in a graph structural
sense.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chan:2013:ARP,
author = "Siu On Chan",
title = "Approximation resistance from pairwise independent
subgroups",
crossref = "ACM:2013:SPF",
pages = "447--456",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488665",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We show optimal (up to constant factor) NP-hardness
for Max-$k$-CSP over any domain, whenever k is larger
than the domain size. This follows from our main result
concerning predicates over abelian groups. We show that
a predicate is approximation resistant if it contains a
subgroup that is balanced pairwise independent. This
gives an unconditional analogue of Austrin--Mossel
hardness result, bypassing the Unique-Games Conjecture
for predicates with an abelian subgroup structure. Our
main ingredient is a new gap-amplification technique
inspired by XOR-lemmas. Using this technique, we also
improve the NP-hardness of approximating
Independent-Set on bounded-degree graphs,
Almost-Coloring, Two-Prover-One-Round-Game, and various
other problems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Huang:2013:ARS,
author = "Sangxia Huang",
title = "Approximation resistance on satisfiable instances for
predicates with few accepting inputs",
crossref = "ACM:2013:SPF",
pages = "457--466",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488666",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove that for all integer $ k \geq 3 $, there is a
predicate P on k Boolean variables with 2$^{\tilde O(k
1 / 3)}$ accepting assignments that is approximation
resistant even on satisfiable instances. That is, given
a satisfiable CSP instance with constraint P, we cannot
achieve better approximation ratio than simply picking
random assignments. This improves the best previously
known result by Hastad and Khot where the predicate has
2$^{O(k 1 / 2)}$ accepting assignments. Our
construction is inspired by several recent
developments. One is the idea of using direct sums to
improve soundness of PCPs, developed by Chan [5]. We
also use techniques from Wenner [32] to construct PCPs
with perfect completeness without relying on the d-to-1
Conjecture.",
acknowledgement = ack-nhfb,
}
@InProceedings{Garg:2013:WEA,
author = "Sanjam Garg and Craig Gentry and Amit Sahai and Brent
Waters",
title = "Witness encryption and its applications",
crossref = "ACM:2013:SPF",
pages = "467--476",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488667",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We put forth the concept of witness encryption. A
witness encryption scheme is defined for an NP language
L (with corresponding witness relation R). In such a
scheme, a user can encrypt a message M to a particular
problem instance x to produce a ciphertext. A recipient
of a ciphertext is able to decrypt the message if x is
in the language and the recipient knows a witness w
where R(x,w) holds. However, if x is not in the
language, then no polynomial-time attacker can
distinguish between encryptions of any two equal length
messages. We emphasize that the encrypter himself may
have no idea whether $x$ is actually in the language.
Our contributions in this paper are threefold. First,
we introduce and formally define witness encryption.
Second, we show how to build several cryptographic
primitives from witness encryption. Finally, we give a
candidate construction based on the NP-complete Exact
Cover problem and Garg, Gentry, and Halevi's recent
construction of ``approximate'' multilinear maps. Our
method for witness encryption also yields the first
candidate construction for an open problem posed by
Rudich in 1989: constructing computational secret
sharing schemes for an NP-complete access structure.",
acknowledgement = ack-nhfb,
}
@InProceedings{De:2013:MSD,
author = "Anindya De and Elchanan Mossel and Joe Neeman",
title = "Majority is stablest: discrete and {SoS}",
crossref = "ACM:2013:SPF",
pages = "477--486",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488668",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The Majority is Stablest Theorem has numerous
applications in hardness of approximation and social
choice theory. We give a new proof of the Majority is
Stablest Theorem by induction on the dimension of the
discrete cube. Unlike the previous proof, it uses
neither the ``invariance principle'' nor Borell's
result in Gaussian space. The new proof is general
enough to include all previous variants of majority is
stablest such as ``it ain't over until it's over'' and
``Majority is most predictable''. Moreover, the new
proof allows us to derive a proof of Majority is
Stablest in a constant level of the Sum of Squares
hierarchy. This implies in particular that Khot-Vishnoi
instance of Max-Cut does not provide a gap instance for
the Lasserre hierarchy.",
acknowledgement = ack-nhfb,
}
@InProceedings{Beck:2013:SEH,
author = "Christopher Beck and Russell Impagliazzo",
title = "Strong {ETH} holds for regular resolution",
crossref = "ACM:2013:SPF",
pages = "487--494",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488669",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We obtain asymptotically sharper lower bounds on
resolution complexity for $k$-CNF's than was known
previously. We show that for any large enough $k$ there
are $k$-CNF's which require resolution width $ (1 -
\tilde O(k^{-1 / 4}))n $, regular resolution size
2$^{(1 - \tilde O(k^{-1 / 4}))n}$, and general
resolution size (3/2)$^{(1 - \tilde O(k - 1 / 4))n}$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lee:2013:NCO,
author = "James R. Lee and Manor Mendel and Mohammad Moharrami",
title = "A node-capacitated {Okamura--Seymour} theorem",
crossref = "ACM:2013:SPF",
pages = "495--504",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488671",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The classical Okamura-Seymour theorem states that for
an edge-capacitated, multi-commodity flow instance in
which all terminals lie on a single face of a planar
graph, there exists a feasible concurrent flow if and
only if the cut conditions are satisfied. Simple
examples show that a similar theorem is impossible in
the node-capacitated setting. Nevertheless, we prove
that an approximate flow/cut theorem does hold: For
some universal $ \epsilon > 0 $, if the node cut
conditions are satisfied, then one can simultaneously
route an $ \epsilon $-fraction of all the demands. This
answers an open question of Chekuri and Kawarabayashi.
More generally, we show that this holds in the setting
of multi-commodity polymatroid networks introduced by
Chekuri, et. al. Our approach employs a new type of
random metric embedding in order to round the convex
programs corresponding to these more general flow
problems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Klein:2013:SRS,
author = "Philip N. Klein and Shay Mozes and Christian Sommer",
title = "Structured recursive separator decompositions for
planar graphs in linear time",
crossref = "ACM:2013:SPF",
pages = "505--514",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488672",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Given a triangulated planar graph $G$ on $n$ vertices
and an integer $r$ $r$-division of $G$ with few holes
is a decomposition of $G$ into $ O(n / r) $ regions of
size at most r such that each region contains at most a
constant number of faces that are not faces of $G$
(also called holes), and such that, for each region,
the total number of vertices on these faces is $
O(\sqrt r) $. We provide an algorithm for computing
$r$-divisions with few holes in linear time. In fact,
our algorithm computes a structure, called
decomposition tree, which represents a recursive
decomposition of $G$ that includes $r$-divisions for
essentially all values of $r$. In particular, given an
exponentially increasing sequence $ \{ \vec r \} =
(r_1, r_2, \ldots {}) $, our algorithm can produce a
recursive $ \{ \vec r \} $-division with few holes in
linear time. $r$-divisions with few holes have been
used in efficient algorithms to compute shortest paths,
minimum cuts, and maximum flows. Our linear-time
algorithm improves upon the decomposition algorithm
used in the state-of-the-art algorithm for minimum
st--cut (Italiano, Nussbaum, Sankowski, and
Wulff-Nilsen, STOC 2011), removing one of the
bottlenecks in the overall running time of their
algorithm (analogously for minimum cut in planar and
bounded-genus graphs).",
acknowledgement = ack-nhfb,
}
@InProceedings{Roditty:2013:FAA,
author = "Liam Roditty and Virginia Vassilevska Williams",
title = "Fast approximation algorithms for the diameter and
radius of sparse graphs",
crossref = "ACM:2013:SPF",
pages = "515--524",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488673",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The diameter and the radius of a graph are fundamental
topological parameters that have many important
practical applications in real world networks. The
fastest combinatorial algorithm for both parameters
works by solving the all-pairs shortest paths problem
(APSP) and has a running time of $ \tilde O(m n) $ in
$m$-edge, $n$-node graphs. In a seminal paper,
Aingworth, Chekuri, Indyk and Motwani [SODA'96 and
SICOMP'99] presented an algorithm that computes in $
\tilde O(m \sqrt n + n^2) $ time an estimate $D$ for
the diameter $D$, such that $ \lfloor 2 / 3 D \rfloor
\leq^D \leq D $. Their paper spawned a long line of
research on approximate APSP. For the specific problem
of diameter approximation, however, no improvement has
been achieved in over 15 years. Our paper presents the
first improvement over the diameter approximation
algorithm of Aingworth et. al, producing an algorithm
with the same estimate but with an expected running
time of $ \tilde O(m \sqrt n) $. We thus show that for
all sparse enough graphs, the diameter can be
3/2-approximated in $ o(n^2) $ time. Our algorithm is
obtained using a surprisingly simple method of
neighborhood depth estimation that is strong enough to
also approximate, in the same running time, the radius
and more generally, all of the eccentricities, i.e. for
every node the distance to its furthest node. We also
provide strong evidence that our diameter approximation
result may be hard to improve. We show that if for some
constant $ \epsilon > 0 $ there is an $ O(m^{2 -
\epsilon }) $ time $ (3 / 2 - \epsilon) $-approximation
algorithm for the diameter of undirected unweighted
graphs, then there is an $ O*((2 - \delta)^n) $ time
algorithm for CNF-SAT on $n$ variables for constant $
\delta > 0 $, and the strong exponential time
hypothesis of [Impagliazzo, Paturi, Zane JCSS'01] is
false. Motivated by this negative result, we give
several improved diameter approximation algorithms for
special cases. We show for instance that for unweighted
graphs of constant diameter $D$ not divisible by $3$,
there is an $ O(m^{2 - \epsilon }) $ time algorithm
that gives a $ (3 / 2 - \epsilon) $ approximation for
constant $ \epsilon > 0 $. This is interesting since
the diameter approximation problem is hardest to solve
for small $D$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Gu:2013:PDM,
author = "Albert Gu and Anupam Gupta and Amit Kumar",
title = "The power of deferral: maintaining a
constant-competitive {Steiner} tree online",
crossref = "ACM:2013:SPF",
pages = "525--534",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488674",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In the online Steiner tree problem, a sequence of
points is revealed one-by-one: when a point arrives, we
only have time to add a single edge connecting this
point to the previous ones, and we want to minimize the
total length of edges added. Here, a tight bound has
been known for two decades: the greedy algorithm
maintains a tree whose cost is $ O(\log n) $ times the
Steiner tree cost, and this is best possible. But
suppose, in addition to the new edge we add, we have
time to change a single edge from the previous set of
edges: can we do much better? Can we, e.g., maintain a
tree that is constant-competitive? We answer this
question in the affirmative. We give a primal-dual
algorithm that makes only a single swap per step (in
addition to adding the edge connecting the new point to
the previous ones), and such that the tree's cost is
only a constant times the optimal cost. Our dual-based
analysis is quite different from previous primal-only
analyses. In particular, we give a correspondence
between radii of dual balls and lengths of tree edges;
since dual balls are associated with points and hence
do not move around (in contrast to edges), we can
closely monitor the edge lengths based on the dual
radii. Showing that these dual radii cannot change too
rapidly is the technical heart of the paper, and allows
us to give a hard bound on the number of swaps per
arrival, while maintaining a constant-competitive tree
at all times. Previous results for this problem gave an
algorithm that performed an amortized constant number
of swaps: for each n, the number of swaps in the first
$n$ steps was O(n). We also give a simpler tight
analysis for this amortized case.",
acknowledgement = ack-nhfb,
}
@InProceedings{Buchbinder:2013:SPE,
author = "Niv Buchbinder and Joseph (Seffi) Naor and Roy
Schwartz",
title = "Simplex partitioning via exponential clocks and the
multiway cut problem",
crossref = "ACM:2013:SPF",
pages = "535--544",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488675",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The Multiway-Cut problem is a fundamental graph
partitioning problem in which the objective is to find
a minimum weight set of edges disconnecting a given set
of special vertices called terminals. This problem is
NP-hard and there is a well known geometric relaxation
in which the graph is embedded into a high dimensional
simplex. Rounding a solution to the geometric
relaxation is equivalent to partitioning the simplex.
We present a novel simplex partitioning algorithm which
is based on em competing exponential clocks and
distortion. Unlike previous methods, it utilizes cuts
that are not parallel to the faces of the simplex.
Applying this partitioning algorithm to the multiway
cut problem, we obtain a simple (4/3)-approximation
algorithm, thus, improving upon the current best known
result. This bound is further pushed to obtain an
approximation factor of 1.32388. It is known that under
the assumption of the unique games conjecture, the best
possible approximation for the Multiway-Cut problem can
be attained via the geometric relaxation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Gorbunov:2013:ABE,
author = "Sergey Gorbunov and Vinod Vaikuntanathan and Hoeteck
Wee",
title = "Attribute-based encryption for circuits",
crossref = "ACM:2013:SPF",
pages = "545--554",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488677",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In an attribute-based encryption (ABE) scheme, a
ciphertext is associated with an $l$-bit public index
pind and a message $m$, and a secret key is associated
with a Boolean predicate $P$. The secret key allows to
decrypt the ciphertext and learn $m$ iff $P({\rm pind})
= 1$. Moreover, the scheme should be secure against
collusions of users, namely, given secret keys for
polynomially many predicates, an adversary learns
nothing about the message if none of the secret keys
can individually decrypt the ciphertext. We present
attribute-based encryption schemes for circuits of any
arbitrary polynomial size, where the public parameters
and the ciphertext grow linearly with the depth of the
circuit. Our construction is secure under the standard
learning with errors (LWE) assumption. Previous
constructions of attribute-based encryption were for
Boolean formulas, captured by the complexity class
${\rm NC}^1 $. In the course of our construction, we
present a new framework for constructing ABE
schemes. As a by-product of our framework, we obtain
ABE schemes for polynomial-size branching programs,
corresponding to the complexity class LOGSPACE, under
quantitatively better assumptions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Goldwasser:2013:RGC,
author = "Shafi Goldwasser and Yael Kalai and Raluca Ada Popa
and Vinod Vaikuntanathan and Nickolai Zeldovich",
title = "Reusable garbled circuits and succinct functional
encryption",
crossref = "ACM:2013:SPF",
pages = "555--564",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488678",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Garbled circuits, introduced by Yao in the mid 80s,
allow computing a function f on an input x without
leaking anything about f or x besides f(x). Garbled
circuits found numerous applications, but every known
construction suffers from one limitation: it offers no
security if used on multiple inputs x. In this paper,
we construct for the first time reusable garbled
circuits. The key building block is a new succinct
single-key functional encryption scheme. Functional
encryption is an ambitious primitive: given an
encryption $ {\rm Enc}(x) $ of a value $x$, and a
secret key $ {\rm sk}_f $ for a function $f$, anyone
can compute $ f(x) $ without learning any other
information about $x$. We construct, for the first
time, a succinct functional encryption scheme for {\em
any} polynomial-time function f where succinctness
means that the ciphertext size does not grow with the
size of the circuit for $f$, but only with its depth.
The security of our construction is based on the
intractability of the Learning with Errors (LWE)
problem and holds as long as an adversary has access to
a single key $ {\rm sk}_f $ (or even an a priori
bounded number of keys for different functions).
Building on our succinct single-key functional
encryption scheme, we show several new applications in
addition to reusable garbled circuits, such as a
paradigm for general function obfuscation which we call
token-based obfuscation, homomorphic encryption for a
class of Turing machines where the evaluation runs in
input-specific time rather than worst-case time, and a
scheme for delegating computation which is publicly
verifiable and maintains the privacy of the
computation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kalai:2013:DBS,
author = "Yael Tauman Kalai and Ran Raz and Ron D. Rothblum",
title = "Delegation for bounded space",
crossref = "ACM:2013:SPF",
pages = "565--574",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488679",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We construct a 1-round delegation scheme for every
language computable in time t=t(n) and space s=s(n),
where the running time of the prover is poly(t) and the
running time of the verifier is $ \tilde O(n + p o l
y(s)) $ (where $ \tilde O $ hides $ \polylog (t) $
factors). The proof exploits a curious connection
between the problem of computation delegation and the
model of multi-prover interactive proofs that are sound
against no-signaling (cheating) strategies, a model
that was studied in the context of multi-prover
interactive proofs with provers that share quantum
entanglement, and is motivated by the physical
principle that information cannot travel faster than
light. For any language computable in time $ t = t(n) $
and space $ s = s(n) $, we construct MIPs that are
sound against no-signaling strategies, where the
running time of the provers is $ \poly (t) $, the
number of provers is $ \tilde O(s) $, and the running
time of the verifier is $ \tilde O(s + n) $. We then
show how to use the method suggested by Aiello et-al
(ICALP, 2000) to convert our MIP into a 1-round
delegation scheme, by using a computational private
information retrieval (PIR) scheme. Thus, assuming the
existence of a sub-exponentially secure PIR scheme, we
get our 1-round delegation scheme.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brakerski:2013:CHL,
author = "Zvika Brakerski and Adeline Langlois and Chris Peikert
and Oded Regev and Damien Stehl{\'e}",
title = "Classical hardness of learning with errors",
crossref = "ACM:2013:SPF",
pages = "575--584",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488680",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We show that the Learning with Errors (LWE) problem is
classically at least as hard as standard worst-case
lattice problems. Previously this was only known under
quantum reductions. Our techniques capture the tradeoff
between the dimension and the modulus of LWE instances,
leading to a much better understanding of the landscape
of the problem. The proof is inspired by techniques
from several recent cryptographic constructions, most
notably fully homomorphic encryption schemes.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ben-Sasson:2013:CEP,
author = "Eli Ben-Sasson and Alessandro Chiesa and Daniel Genkin
and Eran Tromer",
title = "On the concrete efficiency of
probabilistically-checkable proofs",
crossref = "ACM:2013:SPF",
pages = "585--594",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488681",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Probabilistically-Checkable Proofs (PCPs) form the
algorithmic core that enables fast verification of long
computations in many cryptographic constructions. Yet,
despite the wonderful asymptotic savings they bring,
PCPs are also the infamous computational bottleneck
preventing these powerful cryptographic constructions
from being used in practice. To address this problem,
we present several results about the computational
efficiency of PCPs. We construct the first PCP where
the prover and verifier time complexities are
quasi-optimal (i.e., optimal up to poly-logarithmic
factors). The prover and verifier are also
highly-parallelizable, and these computational
guarantees hold even when proving and verifying the
correctness of random-access machine computations. Our
construction is explicit and has the requisite
properties for being used in the cryptographic
applications mentioned above. Next, to better
understand the efficiency of our PCP, we propose a new
efficiency measure for PCPs (and their major
components, locally-testable codes and PCPs of
proximity). We define a concrete-efficiency threshold
that indicates the smallest problem size beyond which
the PCP becomes ``useful'', in the sense that using it
is cheaper than performing naive verification (i.e.,
rerunning the computation); our definition accounts for
both the prover and verifier complexity. We then show
that our PCP has a finite concrete-efficiency
threshold. That such a PCP exists does not follow from
existing works on PCPs with polylogarithmic-time
verifiers. As in [Ben-Sasson and Sudan, STOC '05], PCPs
of proximity for Reed--Solomon (RS) codes are the main
component of our PCP. We construct a PCP of proximity
that reduces the concrete-efficiency threshold for
testing proximity to RS codes from 2$^{683}$ in their
work to 2$^{43}$, which is tantalizingly close to
practicality.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cadek:2013:ECM,
author = "Martin Cadek and Marek Krcal and Jiri Matousek and
Lukas Vokrinek and Uli Wagner",
title = "Extending continuous maps: polynomiality and
undecidability",
crossref = "ACM:2013:SPF",
pages = "595--604",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488683",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider several basic problems of algebraic
topology, with connections to combinatorial and
geometric questions, from the point of view of
computational complexity. The extension problem asks,
given topological spaces $X$, $Y$, a subspace $ A
\subseteq X $, and a (continuous) map $ f : A \to Y $,
whether $f$ can be extended to a map $ X \to Y $. For
computational purposes, we assume that X and Y are
represented as finite simplicial complexes, $A$ is a
subcomplex of $X$, and $f$ is given as a simplicial
map. In this generality the problem is undecidable, as
follows from Novikov's result from the 1950s on
uncomputability of the fundamental group $ \pi_1 (Y) $.
We thus study the problem under the assumption that,
for some $ k \geq 2 $, $Y$ is $ (k - 1) $-connected;
informally, this means that $Y$ has ``no holes up to
dimension $ k - 1 $'' i.e., the first $ k - 1 $
homotopy groups of $Y$ vanish (a basic example of such
a $Y$ is the sphere $ S^k $). We prove that, on the
one hand, this problem is still undecidable for $ \dim
X = 2 k $. On the other hand, for every fixed $ k \geq
2 $, we obtain an algorithm that solves the extension
problem in polynomial time assuming $Y$ $ (k - 1)
$-connected and $ \dim X \leq 2 k - 1 $. For $ \dim X
\leq 2 k - 2 $, the algorithm also provides a
classification of all extensions up to homotopy
(continuous deformation). This relies on results of our
SODA 2012 paper, and the main new ingredient is a
machinery of objects with polynomial-time homology,
which is a polynomial-time analog of objects with
effective homology developed earlier by Sergeraert et
al. We also consider the computation of the higher
homotopy groups $ \pi_k (Y) $, $ k \geq 2 $, for a
1-connected $Y$. Their computability was established by
Brown in 1957; we show that $ \pi_k(Y) $ can be
computed in polynomial time for every fixed $ k \geq 2
$. On the other hand, Anick proved in 1989 that
computing $ \pi_k(Y) $ is \#P-hard if $k$ is a part of
input, where $Y$ is a cell complex with certain rather
compact encoding. We strengthen his result to
\#P-hardness for $Y$ given as a simplicial complex.",
acknowledgement = ack-nhfb,
}
@InProceedings{Har-Peled:2013:NPL,
author = "Sariel Har-Peled and Benjamin Adam Raichel",
title = "Net and prune: a linear time algorithm for {Euclidean}
distance problems",
crossref = "ACM:2013:SPF",
pages = "605--614",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488684",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We provide a general framework for getting linear time
constant factor approximations (and in many cases
FPTAS's) to a copious amount of well known and well
studied problems in Computational Geometry, such as
$k$-center clustering and furthest nearest neighbor.
The new approach is robust to variations in the input
problem, and yet it is simple, elegant and practical.
In particular, many of these well studied problems
which fit easily into our framework, either previously
had no linear time approximation algorithm, or required
rather involved algorithms and analysis. A short list
of the problems we consider include furthest nearest
neighbor, $k$-center clustering, smallest disk
enclosing k points, $k$-th largest distance, $k$-th
smallest $m$-nearest neighbor distance, $k$-th heaviest
edge in the MST and other spanning forest type
problems, problems involving upward closed set systems,
and more. Finally, we show how to extend our framework
such that the linear running time bound holds with high
probability.",
acknowledgement = ack-nhfb,
}
@InProceedings{Caputo:2013:RLT,
author = "Pietro Caputo and Fabio Martinelli and Alistair
Sinclair and Alexandre Stauffer",
title = "Random lattice triangulations: structure and
algorithms",
crossref = "ACM:2013:SPF",
pages = "615--624",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488685",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The paper concerns lattice triangulations, i.e.,
triangulations of the integer points in a polygon in $
R^2 $ whose vertices are also integer points. Lattice
triangulations have been studied extensively both as
geometric objects in their own right and by virtue of
applications in algebraic geometry. Our focus is on
random triangulations in which a triangulation $ \sigma
$ has weight $ \lambda^{| \sigma |} $, where $ \lambda
$ is a positive real parameter and $ | \sigma | $ is
the total length of the edges in $ \sigma $.
Empirically, this model exhibits a ``phase transition''
at $ \lambda = 1 $ (corresponding to the uniform
distribution): for $ \lambda < 1 $ distant edges behave
essentially independently, while for $ \lambda > 1 $
very large regions of aligned edges appear. We
substantiate this picture as follows. For $ \lambda < 1
$ sufficiently small, we show that correlations between
edges decay exponentially with distance (suitably
defined), and also that the Glauber dynamics (a local
Markov chain based on flipping edges) is rapidly mixing
(in time polynomial in the number of edges). This
dynamics has been proposed by several authors as an
algorithm for generating random triangulations. By
contrast, for $ \lambda > 1 $ we show that the mixing
time is exponential. These are apparently the first
rigorous quantitative results on spatial mixing
properties and dynamics of random lattice
triangulations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sinclair:2013:LYT,
author = "Alistair Sinclair and Piyush Srivastava",
title = "{Lee--Yang} theorems and the complexity of computing
averages",
crossref = "ACM:2013:SPF",
pages = "625--634",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488686",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the complexity of computing average
quantities related to spin systems, such as the mean
magnetization and susceptibility in the ferromagnetic
Ising model, and the average dimer count (or average
size of a matching) in the monomer-dimer model. By
establishing connections between the complexity of
computing these averages and the location of the
complex zeros of the partition function, we show that
these averages are \#P-hard to compute. In case of the
Ising model, our approach requires us to prove an
extension of the famous Lee--Yang Theorem from the
1950s.",
acknowledgement = ack-nhfb,
}
@InProceedings{Cai:2013:CDR,
author = "Jin-Yi Cai and Heng Guo and Tyson Williams",
title = "A complete dichotomy rises from the capture of
vanishing signatures: extended abstract",
crossref = "ACM:2013:SPF",
pages = "635--644",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488687",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We prove a complexity dichotomy theorem for Holant
problems over an arbitrary set of complex-valued
symmetric constraint functions {F} on Boolean
variables. This extends and unifies all previous
dichotomies for Holant problems on symmetric constraint
functions (taking values without a finite modulus). We
define and characterize all symmetric vanishing
signatures. They turned out to be essential to the
complete classification of Holant problems. The
dichotomy theorem has an explicit tractability
criterion. A Holant problem defined by a set of
constraint functions {F} is solvable in polynomial time
if it satisfies this tractability criterion, and is
\#P-hard otherwise. The tractability criterion can be
intuitively stated as follows: A set {F} is tractable
if (1) every function in {F} has arity at most two, or
(2) {F} is transformable to an affine type, or (3) {F}
is transformable to a product type, or (4) {F} is
vanishing, combined with the right type of binary
functions, or (5) {F} belongs to a special category of
vanishing type Fibonacci gates. The proof of this
theorem utilizes many previous dichotomy theorems on
Holant problems and Boolean \#CSP. Holographic
transformations play an indispensable role, not only as
a proof technique, but also in the statement of the
dichotomy criterion.",
acknowledgement = ack-nhfb,
}
@InProceedings{Miller:2013:SLO,
author = "Gary L. Miller",
title = "Solving large optimization problems using spectral
graph theory",
crossref = "ACM:2013:SPF",
pages = "981--981",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488689",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Spectral Graph Theory is the interplay between linear
algebra and combinatorial graph theory. One application
of this interplay is a nearly linear time solver for
Symmetric Diagonally Dominate systems (SDD). This
seemingly restrictive class of systems has received
much interest in the last 15 years. Both algorithm
design theory and practical implementations have made
substantial progress. There is also a growing number of
problems that can be efficiently solved using SDD
solvers including: image segmentation, image denoising,
finding solutions to elliptic equations, computing
maximum flow in a graph, graph sparsification, and
graphics. All these examples can be viewed as special
case of convex optimization problems.",
acknowledgement = ack-nhfb,
}
@InProceedings{Elkin:2013:OES,
author = "Michael Elkin and Shay Solomon",
title = "Optimal {Euclidean} spanners: really short, thin and
lanky",
crossref = "ACM:2013:SPF",
pages = "645--654",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488691",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The degree, the (hop-)diameter, and the weight are the
most basic and well-studied parameters of geometric
spanners. In a seminal STOC'95 paper, titled
``Euclidean spanners: short, thin and lanky'', Arya et
al. [2] devised a construction of Euclidean $ (1 +
\epsilon) $-spanners that achieves constant degree,
diameter $ O(\log n) $, weight $ O(\log^2 n) \cdot
\omega ({\rm MST}) $, and has running time $ O(n \cdot
\log n) $. This construction applies to $n$-point
constant-dimensional Euclidean spaces. Moreover, Arya
et al. conjectured that the weight bound can be
improved by a logarithmic factor, without increasing
the degree and the diameter of the spanner, and within
the same running time. This conjecture of Arya et al.
became one of the most central open problems in the
area of Euclidean spanners. Nevertheless, the only
progress since 1995 towards its resolution was achieved
in the lower bounds front: Any spanner with diameter $
O(\log n) $ must incur weight $ \Omega (\log n) \cdot
\omega ({\rm MST}) $, and this lower bound holds
regardless of the stretch or the degree of the spanner
[12, 1]. In this paper we resolve the long-standing
conjecture of Arya et al. in the affirmative. We
present a spanner construction with the same stretch,
degree, diameter, and running time, as in Arya et al.'s
result, but with optimal weight $ O(\log n) \cdot
\omega ({\rm MST}) $. So our spanners are as thin and
lanky as those of Arya et al., but they are really
short! Moreover, our result is more general in three
ways. First, we demonstrate that the conjecture holds
true not only in constant-dimensional Euclidean spaces,
but also in doubling metrics. Second, we provide a
general tradeoff between the three involved parameters,
which is tight in the entire range. Third, we devise a
transformation that decreases the lightness of spanners
in general metrics, while keeping all their other
parameters in check. Our main result is obtained as a
corollary of this transformation.",
acknowledgement = ack-nhfb,
}
@InProceedings{Feldman:2013:SAL,
author = "Vitaly Feldman and Elena Grigorescu and Lev Reyzin and
Santosh Vempala and Ying Xiao",
title = "Statistical algorithms and a lower bound for detecting
planted cliques",
crossref = "ACM:2013:SPF",
pages = "655--664",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488692",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We introduce a framework for proving lower bounds on
computational problems over distributions, based on a
class of algorithms called statistical algorithms. For
such algorithms, access to the input distribution is
limited to obtaining an estimate of the expectation of
any given function on a sample drawn randomly from the
input distribution, rather than directly accessing
samples. Most natural algorithms of interest in theory
and in practice, e.g., moments-based methods, local
search, standard iterative methods for convex
optimization, MCMC and simulated annealing, are
statistical algorithms or have statistical
counterparts. Our framework is inspired by and
generalize the statistical query model in learning
theory [34]. Our main application is a nearly optimal
lower bound on the complexity of any statistical
algorithm for detecting planted bipartite clique
distributions (or planted dense subgraph distributions)
when the planted clique has size $ O(n^{1 / 2 -
\delta}) $ for any constant $ \delta > 0 $. Variants of
these problems have been assumed to be hard to prove
hardness for other problems and for cryptographic
applications. Our lower bounds provide concrete
evidence of hardness, thus supporting these
assumptions.",
acknowledgement = ack-nhfb,
}
@InProceedings{Jain:2013:LRM,
author = "Prateek Jain and Praneeth Netrapalli and Sujay
Sanghavi",
title = "Low-rank matrix completion using alternating
minimization",
crossref = "ACM:2013:SPF",
pages = "665--674",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488693",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Alternating minimization represents a widely
applicable and empirically successful approach for
finding low-rank matrices that best fit the given data.
For example, for the problem of low-rank matrix
completion, this method is believed to be one of the
most accurate and efficient, and formed a major
component of the winning entry in the Netflix Challenge
[17]. In the alternating minimization approach, the
low-rank target matrix is written in a bi-linear form,
i.e. X = UV$^+$; the algorithm then alternates between
finding the best U and the best V. Typically, each
alternating step in isolation is convex and tractable.
However the overall problem becomes non-convex and is
prone to local minima. In fact, there has been almost
no theoretical understanding of when this approach
yields a good result. In this paper we present one of
the first theoretical analyses of the performance of
alternating minimization for matrix completion, and the
related problem of matrix sensing. For both these
problems, celebrated recent results have shown that
they become well-posed and tractable once certain (now
standard) conditions are imposed on the problem. We
show that alternating minimization also succeeds under
similar conditions. Moreover, compared to existing
results, our paper shows that alternating minimization
guarantees faster (in particular, geometric)
convergence to the true matrix, while allowing a
significantly simpler analysis.",
acknowledgement = ack-nhfb,
}
@InProceedings{Alon:2013:ARM,
author = "Noga Alon and Troy Lee and Adi Shraibman and Santosh
Vempala",
title = "The approximate rank of a matrix and its algorithmic
applications: approximate rank",
crossref = "ACM:2013:SPF",
pages = "675--684",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488694",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the $ \epsilon $-rank of a real matrix A,
defined for any $ \epsilon > 0 $ as the minimum rank
over matrices that approximate every entry of $A$ to
within an additive $ \epsilon $. This parameter is
connected to other notions of approximate rank and is
motivated by problems from various topics including
communication complexity, combinatorial optimization,
game theory, computational geometry and learning
theory. Here we give bounds on the $ \epsilon $-rank
and use them for algorithmic applications. Our main
algorithmic results are (a) polynomial-time additive
approximation schemes for Nash equilibria for 2-player
games when the payoff matrices are positive
semidefinite or have logarithmic rank and (b) an
additive PTAS for the densest subgraph problem for
similar classes of weighted graphs. We use
combinatorial, geometric and spectral techniques; our
main new tool is an algorithm for efficiently covering
a convex body with translates of another convex body.",
acknowledgement = ack-nhfb,
}
@InProceedings{Harris:2013:CSP,
author = "David G. Harris and Aravind Srinivasan",
title = "Constraint satisfaction, packet routing, and the
{Lovasz} local lemma",
crossref = "ACM:2013:SPF",
pages = "685--694",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488696",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Constraint-satisfaction problems (CSPs) form a basic
family of NP-hard optimization problems that includes
satisfiability. Motivated by the sufficient condition
for the satisfiability of SAT formulae that is offered
by the Lovasz Local Lemma, we seek such sufficient
conditions for arbitrary CSPs. To this end, we identify
a variable-covering radius--type parameter for the
infeasible configurations of a given CSP, and also
develop an extension of the Lovasz Local Lemma in which
many of the events to be avoided have probabilities
arbitrarily close to one; these lead to a general
sufficient condition for the satisfiability of
arbitrary CSPs. One primary application is to
packet-routing in the classical Leighton-Maggs-Rao
setting, where we introduce several additional ideas in
order to prove the existence of near-optimal schedules;
further applications in combinatorial optimization are
also shown.",
acknowledgement = ack-nhfb,
}
@InProceedings{Thapper:2013:CFV,
author = "Johan Thapper and Stanislav Zivny",
title = "The complexity of finite-valued {CSPs}",
crossref = "ACM:2013:SPF",
pages = "695--704",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488697",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Let $ \Gamma $ be a set of rational-valued functions
on a fixed finite domain; such a set is called a
finite-valued constraint language. The valued
constraint satisfaction problem, VCSP( $ \Gamma $), is
the problem of minimising a function given as a sum of
functions from $ \Gamma $ . We establish a dichotomy
theorem with respect to exact solvability for all
finite-valued languages defined on domains of arbitrary
finite size. We show that every core language $ \Gamma
$ either admits a binary idempotent and symmetric
fractional polymorphism in which case the basic linear
programming relaxation solves any instance of VCSP( $
\Gamma $) exactly, or $ \Gamma $ satisfies a simple
hardness condition that allows for a polynomial-time
reduction from Max-Cut to VCSP( $ \Gamma $). In other
words, there is a single algorithm for all tractable
cases and a single reason for intractability. Our
results show that for exact solvability of VCSPs the
basic linear programming relaxation suffices and
semidefinite relaxations do not add any power. Our
results generalise all previous partial classifications
of finite-valued languages: the classification of
{0,1}-valued languages containing all unary functions
obtained by Deineko et al. [JACM'06]; the
classifications of {0,1}-valued languages on
two-element, three-element, and four-element domains
obtained by Creignou [JCSS'95], Jonsson et al.
[SICOMP'06], and Jonsson et al.[CP'11], respectively;
the classifications of finite-valued languages on
two-element and three-element domains obtained by Cohen
et al. [AIJ'06] and Huber et al. [SODA'13],
respectively; the classification of finite-valued
languages containing all {0,1}-valued unary functions
obtained by Kolmogorov and Zivny [JACM'13]; and the
classification of Min-0-Ext problems obtained by Hirai
[SODA'13].",
acknowledgement = ack-nhfb,
}
@InProceedings{Coja-Oghlan:2013:GAK,
author = "Amin Coja-Oghlan and Konstantinos Panagiotou",
title = "Going after the {k-SAT} threshold",
crossref = "ACM:2013:SPF",
pages = "705--714",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488698",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Random $k$-SAT is the single most intensely studied
example of a random constraint satisfaction problem.
But despite substantial progress over the past decade,
the threshold for the existence of satisfying
assignments is not known precisely for any $ k \geq 3
$. The best current results, based on the second moment
method, yield upper and lower bounds that differ by an
additive $ k \cdot {\ln 2} / 2 $, a term that is
unbounded in $k$ (Achlioptas, Peres: STOC 2003). The
basic reason for this gap is the inherent asymmetry of
the Boolean values 'true' and 'false' in contrast to
the perfect symmetry, e.g., among the various colors in
a graph coloring problem. Here we develop a new
asymmetric second moment method that allows us to
tackle this issue head on for the first time in the
theory of random CSPs. This technique enables us to
compute the $k$-SAT threshold up to an additive $ \ln 2
- 1 / 2 + O(1 / k) \sim 0.19 $. Independently of the
rigorous work, physicists have developed a
sophisticated but non-rigorous technique called the
``cavity method'' for the study of random CSPs (Mezard,
Parisi, Zecchina: Science~2002). Our result matches the
best bound that can be obtained from the so-called
``replica symmetric'' version of the cavity method, and
indeed our proof directly harnesses parts of the
physics calculations.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kol:2013:ICC,
author = "Gillat Kol and Ran Raz",
title = "Interactive channel capacity",
crossref = "ACM:2013:SPF",
pages = "715--724",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488699",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the interactive channel capacity of an $
\epsilon $-noisy channel. The interactive channel
capacity $ C(\epsilon) $ is defined as the minimal
ratio between the communication complexity of a problem
(over a non-noisy channel), and the communication
complexity of the same problem over the binary
symmetric channel with noise rate $ \epsilon $, where
the communication complexity tends to infinity. Our
main result is the upper bound $ C(\epsilon) \leq 1 -
\Omega (\sqrt H(\epsilon)) $. This compares with
Shannon's non-interactive channel capacity of $ 1 -
H(\epsilon) $. In particular, for a small enough $
\epsilon $, our result gives the first separation
between interactive and non-interactive channel
capacity, answering an open problem by Schulman
[Schulman1]. We complement this result by the lower
bound $ C(\epsilon) \geq 1 - O(\sqrt H(\epsilon)) $,
proved for the case where the players take alternating
turns.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bernstein:2013:MSP,
author = "Aaron Bernstein",
title = "Maintaining shortest paths under deletions in weighted
directed graphs: [extended abstract]",
crossref = "ACM:2013:SPF",
pages = "725--734",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488701",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present an improved algorithm for maintaining
all-pairs $ 1 + \epsilon $ approximate shortest paths
under deletions and weight-increases. The previous
state of the art for this problem was total update time
$ \tilde O (n^2 \sqrt m / \epsilon) $ for directed,
unweighted graphs [2], and $ \tilde O(m n / \epsilon) $
for undirected, unweighted graphs [12]. Both algorithms
were randomized and had constant query time. Note that
$ \tilde O(m n) $ is a natural barrier because even
with a $ (1 + \epsilon) $ approximation, there is no $
o(m n) $ combinatorial algorithm for the static
all-pairs shortest path problem. Our algorithm works on
directed, weighted graphs and has total (randomized)
update time $ \tilde O (m n \log (R) / \epsilon) $
where $R$ is the ratio of the largest edge weight ever
seen in the graph, to the smallest such weight (our
query time is constant). Note that $ \log (R) = O(\log
(n)) $ as long as weights are polynomial in $n$.
Although $ \tilde O(m n \log (R) / \epsilon) $ is the
total time over all updates, our algorithm also
requires a clearly unavoidable constant time per
update. Thus, we effectively expand the $ \tilde O(m n)
$ total update time bound from undirected, unweighted
graphs to directed graphs with polynomial weights. This
is in fact the first non-trivial algorithm for
decremental all-pairs shortest paths that works on
weighted graphs (previous algorithms could only handle
small integer weights). By a well known reduction from
decremental algorithms to fully dynamic ones [9], our
improved decremental algorithm leads to improved
query-update tradeoffs for fully dynamic $ (1 +
\epsilon) $ approximate APSP algorithm in directed
graphs.",
acknowledgement = ack-nhfb,
}
@InProceedings{Eisenstat:2013:LTA,
author = "David Eisenstat and Philip N. Klein",
title = "Linear-time algorithms for max flow and
multiple-source shortest paths in unit-weight planar
graphs",
crossref = "ACM:2013:SPF",
pages = "735--744",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488702",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give simple linear-time algorithms for two problems
in planar graphs: max st-flow in directed graphs with
unit capacities, and multiple-source shortest paths in
undirected graphs with unit lengths.",
acknowledgement = ack-nhfb,
}
@InProceedings{Neiman:2013:SDA,
author = "Ofer Neiman and Shay Solomon",
title = "Simple deterministic algorithms for fully dynamic
maximal matching",
crossref = "ACM:2013:SPF",
pages = "745--754",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488703",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A maximal matching can be maintained in fully dynamic
(supporting both addition and deletion of edges)
$n$-vertex graphs using a trivial deterministic
algorithm with a worst-case update time of $ O(n) $. No
deterministic algorithm that outperforms the naive $
O(n) $ one was reported up to this date. The only
progress in this direction is due to Ivkovic and Lloyd
[14], who in 1993 devised a deterministic algorithm
with an amortized update time of O((n+m)$^{ \sqrt 2 /
2}$), where m is the number of edges. In this paper we
show the first deterministic fully dynamic algorithm
that outperforms the trivial one. Specifically, we
provide a deterministic worst-case update time of $
O(\sqrt m) $. Moreover, our algorithm maintains a
matching which is in fact a 3/2-approximate maximum
cardinality matching (MCM). We remark that no fully
dynamic algorithm for maintaining $ (2 - \epsilon)
$-approximate MCM improving upon the naive $ O(n) $ was
known prior to this work, even allowing amortized time
bounds and randomization. For low arboricity graphs
(e.g., planar graphs and graphs excluding fixed
minors), we devise another simple deterministic
algorithm with sub-logarithmic update time.
Specifically, it maintains a fully dynamic maximal
matching with amortized update time of $ O(\log n /
\log \log n) $. This result addresses an open question
of Onak and Rubinfeld [19]. We also show a
deterministic algorithm with optimal space usage of $
O(n + m) $, that for arbitrary graphs maintains a
maximal matching with amortized update time of $
O(\sqrt m) $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Lee:2013:NAC,
author = "Yin Tat Lee and Satish Rao and Nikhil Srivastava",
title = "A new approach to computing maximum flows using
electrical flows",
crossref = "ACM:2013:SPF",
pages = "755--764",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488704",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We give an algorithm which computes a $ (1 - \epsilon)
$-approximately maximum st-flow in an undirected
uncapacitated graph in time $ O(1 / \epsilon \sqrt m /
F \cdot m \log^2 n) $ where $F$ is the flow value. By
trading this off against the Karger-Levine algorithm
for undirected graphs which takes $ \tilde O(m + n F) $
time, we obtain a running time of $ \tilde O(m n^{1 /
3} / \epsilon^{2 / 3}) $ for uncapacitated graphs,
improving the previous best dependence on $ \epsilon $
by a factor of $ O(1 / \epsilon^3) $. Like the
algorithm of Christiano, Kelner, Madry, Spielman and
Teng, our algorithm reduces the problem to electrical
flow computations which are carried out in linear time
using fast Laplacian solvers. However, in contrast to
previous work, our algorithm does not reweight the
edges of the graph in any way, and instead uses local
(i.e., non s-t) electrical flows to reroute the flow on
congested edges. The algorithm is simple and may be
viewed as trying to find a point at the intersection of
two convex sets (the affine subspace of st-flows of
value $F$ and the $ l_\infty $ ball) by an accelerated
version of the method of alternating projections due to
Nesterov. By combining this with Ford and Fulkerson's
augmenting paths algorithm, we obtain an exact
algorithm with running time $ \tilde O(m^{5 / 4} F^{1 /
4}) $ for uncapacitated undirected graphs, improving
the previous best running time of $ \tilde O(m + \min
(n F, m^{3 / 2})) $. We give a related algorithm with
the same running time for approximate minimum cut,
based on minimizing a smoothed version of the $ l_1 $
norm inside the cut space of the input graph. We show
that the minimizer of this norm is related to an
approximate blocking flow and use this to give an
algorithm for computing a length $k$ approximately
blocking flow in time $ \tilde O(m \sqrt k) $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Orlin:2013:MFN,
author = "James B. Orlin",
title = "{Max} flows in {$ O(n m) $} time, or better",
crossref = "ACM:2013:SPF",
pages = "765--774",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488705",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In this paper, we present improved polynomial time
algorithms for the max flow problem defined on sparse
networks with $n$ nodes and $m$ arcs. We show how to
solve the max flow problem in $ O(n m + m^{31 / 16}
\log^2 n) $ time. In the case that $ m = O(n^{1.06}) $,
this improves upon the best previous algorithm due to
King, Rao, and Tarjan, who solved the max flow problem
in $ O(n m \log_{m / (n \log n)} n) $ time. This
establishes that the max flow problem is solvable in $
O(n m) $ time for all values of $n$ and $m$. In the
case that $ m = O(n) $, we improve the running time to
$ O(n^2 / \log n) $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bringmann:2013:SSD,
author = "Karl Bringmann and Kasper Green Larsen",
title = "Succinct sampling from discrete distributions",
crossref = "ACM:2013:SPF",
pages = "775--782",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488707",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We revisit the classic problem of sampling from a
discrete distribution: Given n non-negative w-bit
integers x$_1$ ,..,x$_n$, the task is to build a data
structure that allows sampling i with probability
proportional to x$_i$. The classic solution is Walker's
alias method that takes, when implemented on a Word
RAM, $ O(n) $ preprocessing time, $ O(1) $ expected
query time for one sample, and $ n(w + 2 \lg (n) +
o(1)) $ bits of space. Using the terminology of
succinct data structures, this solution has redundancy
$ 2 n \lg (n) + o(n) $ bits, i.e., it uses $ 2 n \lg
(n) + o(n) $ bits in addition to the information
theoretic minimum required for storing the input. In
this paper, we study whether this space usage can be
improved. In the systematic case, in which the input is
read-only, we present a novel data structure using $ r
+ O(w) $ redundant bits, $ O(n / r) $ expected query
time and $ O(n) $ preprocessing time for any $r$. This
is an improvement in redundancy by a factor of $ \Omega
(\log n) $ over the alias method for $ r = n $, even
though the alias method is not systematic. Moreover, we
complement our data structure with a lower bound
showing that this trade-off is tight for systematic
data structures. In the non-systematic case, in which
the input numbers may be represented in more clever
ways than just storing them one-by-one, we demonstrate
a very surprising separation from the systematic case:
With only 1 redundant bit, it is possible to support
optimal $ O(1) $ expected query time and $ O(n) $
preprocessing time! On the one hand, our results
improve upon the space requirement of the classic
solution for a fundamental sampling problem, on the
other hand, they provide the strongest known separation
between the systematic and non-systematic case for any
data structure problem. Finally, we also believe our
upper bounds are practically efficient and simpler than
Walker's alias method.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2013:NIS,
author = "Xin Li",
title = "New independent source extractors with exponential
improvement",
crossref = "ACM:2013:SPF",
pages = "783--792",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488708",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the problem of constructing explicit
extractors for independent general weak random sources.
For weak sources on $n$ bits with min-entropy $k$,
previously the best known extractor needs to use at
least $ \log n / \log k $ independent sources [22, 3].
In this paper we give a new extractor that only uses $
O(\log (\log n / \log k)) + O(1) $ independent sources.
Thus, our result improves the previous best result
exponentially. We then use our new extractor to give
improved network extractor protocols, as defined in
[14]. The network extractor protocols also give new
results in distributed computing with general weak
random sources, which dramatically improve previous
results. For example, we can tolerate a nearly optimal
fraction of faulty players in synchronous Byzantine
agreement and leader election, even if the players only
have access to independent $n$-bit weak random sources
with min-entropy as small as $ k = \polylog (n) $. Our
extractor for independent sources is based on a new
condenser for somewhere random sources with a special
structure. We believe our techniques are interesting in
their own right and are promising for further
improvement.",
acknowledgement = ack-nhfb,
}
@InProceedings{Rothblum:2013:IPP,
author = "Guy N. Rothblum and Salil Vadhan and Avi Wigderson",
title = "Interactive proofs of proximity: delegating
computation in sublinear time",
crossref = "ACM:2013:SPF",
pages = "793--802",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488709",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study interactive proofs with sublinear-time
verifiers. These proof systems can be used to ensure
approximate correctness for the results of computations
delegated to an untrusted server. Following the
literature on property testing, we seek proof systems
where with high probability the verifier accepts every
input in the language, and rejects every input that is
far from the language. The verifier's query complexity
(and computation complexity), as well as the
communication, should all be sublinear. We call such a
proof system an Interactive Proof of Proximity (IPP).
On the positive side, our main result is that all
languages in NC have Interactive Proofs of Proximity
with roughly $ \sqrt n $ query and communication and
complexities, and $ \polylog (n) $ communication
rounds. This is achieved by identifying a natural
language, membership in an affine subspace (for a
structured class of subspaces), that is complete for
constructing interactive proofs of proximity, and
providing efficient protocols for it. In building an
IPP for this complete language, we show a tradeoff
between the query and communication complexity and the
number of rounds. For example, we give a 2-round
protocol with roughly $ n^{3 / 4} $ queries and
communication. On the negative side, we show that there
exist natural languages in N$ C^1 $, for which the sum
of queries and communication in any constant-round
interactive proof of proximity must be polynomially
related to $n$. In particular, for any 2-round
protocol, the sum of queries and communication must be
at least $ \tilde \Omega (\sqrt n) $. Finally, we
construct much better IPPs for specific functions, such
as bipartiteness on random or well-mixing graphs, and
the majority function. The query complexities of these
protocols are provably better (by exponential or
polynomial factors) than what is possible in the
standard property testing model, i.e. without a
prover.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ajtai:2013:LBR,
author = "Miklos Ajtai",
title = "Lower bounds for {RAMs} and quantifier elimination",
crossref = "ACM:2013:SPF",
pages = "803--812",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488710",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "For each natural number $d$ we consider a finite
structure $ M_d $ whose universe is the set of all $ 0,
1 $-sequence of length $ n = 2^d $, each representing a
natural number in the set $ \{ 0, 1, \ldots {}, 2^n - 1
\} $ in binary form. The operations included in the
structure are the four constants $ 0, 1, 2^n - 1, n $,
multiplication and addition modulo $ 2^n $, the unary
function $ \{ \min 2^x, 2^n - 1 \} $, the binary
functions $ \lfloor x / y \rfloor $ (with $ \lfloor x /
0 \rfloor = 0 $), $ \max (x, y) $, $ \min (x, y) $,
and the boolean vector operations, $ {\rm vee} $, $-$
defined on $ 0, 1 $ sequences of length $n$, by
performing the operations on all components
simultaneously. These are essentially the arithmetic
operations that can be performed on a RAM, with
wordlength $n$, by a single instruction. We show that
there exists an $ \epsilon > 0 $ and a term (that is,
an algebraic expression) $ F(x, y) $ built up from the
mentioned operations, with the only free variables $x$,
$y$, such that if $ G_d(y), d = 0, 1, 2, \ldots {} $,
is a sequence of terms, and for all $ d = 0, 1, 2,
\ldots {}, M_d $ models $ \forall x, [G_d (x) \to
\exists y, F(x, y) = 0] $, then for infinitely many
integers $d$, the depth of the term $ G_d $, that is,
the maximal number of nestings of the operations in it,
is at least $ \epsilon (\log d)^{1 / 2} = \epsilon
(\log \log n)^{1 / 2} $. The following is a
consequence. We are considering RAMs $ N_n $, with
wordlength $ n = 2^d $, whose arithmetic instructions
are the arithmetic operations listed above, and also
have the usual other RAM instructions. The size of the
memory is restricted only by the address space, that
is, it is $ 2^n $ words. The RAMs has a finite
instruction set, each instruction is encoded by a fixed
natural number independently of $n$. Therefore a
program $P$ can run on each machine $ N_n $, if $ n =
2^d $ is sufficiently large. We show that there exists
an $ \epsilon > 0 $ and a program $P$, such that it
satisfies the following two conditions. (i) For all
sufficiently large $ n = 2^d $, if $P$ running on N$_n$
gets an input consisting of two words $a$ and $b$,
then, in constant time, it gives a $ 0, 1 $ output $
P_n(a, b) $. (ii) Suppose that $Q$ is a program such
that for each sufficiently large $ n = 2^d $, if $Q$,
running on $ N_n $, gets a word $a$ of length $n$ as an
input, then it decides whether there exists a word $b$
of length $n$ such that $ P_n(a, b) = 0. $ Then, for
infinitely many positive integers $d$, there exists a
word $a$ of length $ n = 2^d $, such that the running
time of $Q$ on $ N_n $ at input $a$ is at least $
\epsilon (\log d)^{1 / 2} (\log \log d)^{-1} \geq (\log
d)^{1 / 2 - \epsilon } = (\log \log n)^{1 / 2 -
\epsilon } $.",
acknowledgement = ack-nhfb,
}
@InProceedings{Beck:2013:STR,
author = "Chris Beck and Jakob Nordstrom and Bangsheng Tang",
title = "Some trade-off results for polynomial calculus:
extended abstract",
crossref = "ACM:2013:SPF",
pages = "813--822",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488711",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present size-space trade-offs for the polynomial
calculus (PC) and polynomial calculus resolution (PCR)
proof systems. These are the first true size-space
trade-offs in any algebraic proof system, showing that
size and space cannot be simultaneously optimized in
these models. We achieve this by extending essentially
all known size-space trade-offs for resolution to PC
and PCR. As such, our results cover space complexity
from constant all the way up to exponential and yield
mostly superpolynomial or even exponential size
blow-ups. Since the upper bounds in our trade-offs hold
for resolution, our work shows that there are formulas
for which adding algebraic reasoning on top of
resolution does not improve the trade-off properties in
any significant way. As byproducts of our analysis, we
also obtain trade-offs between space and degree in PC
and PCR exactly matching analogous results for space
versus width in resolution, and strengthen the
resolution trade-offs in [Beame, Beck, and Impagliazzo
'12] to apply also to $k$-CNF formulas.",
acknowledgement = ack-nhfb,
}
@InProceedings{Bhowmick:2013:NBM,
author = "Abhishek Bhowmick and Zeev Dvir and Shachar Lovett",
title = "New bounds for matching vector families",
crossref = "ACM:2013:SPF",
pages = "823--832",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488713",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A Matching Vector (MV) family modulo m is a pair of
ordered lists $ U = (u_1, \ldots {}, u_t) $ and $ V =
(v_1, \ldots {}, v_t) $ where $ u_i, v_j \in Z_m^n $
with the following inner product pattern: for any $ i,
\{ u_i, v_i \} = 0 $, and for any $ i \neq j $, $ \{
u_i, v_j \} \neq 0 $. A MV family is called
$q$-restricted if inner products $ \{ u_i, v_j \} $
take at most $q$ different values. Our interest in MV
families stems from their recent application in the
construction of sub-exponential locally decodable codes
(LDCs). There, $q$-restricted MV families are used to
construct LDCs with $q$ queries, and there is special
interest in the regime where $q$ is constant. When $m$
is a prime it is known that such constructions yield
codes with exponential block length. However, for
composite $m$ the behaviour is dramatically different.
A recent work by Efremenko [8] (based on an approach
initiated by Yekhanin [24]) gives the first
sub-exponential LDC with constant queries. It is based
on a construction of a MV family of super-polynomial
size by Grolmusz [10] modulo composite $m$. In this
work, we prove two lower bounds on the block length of
LDCs which are based on black box construction using MV
families. When $q$ is constant (or sufficiently small),
we prove that such LDCs must have a quadratic block
length. When the modulus $m$ is constant (as it is in
the construction of Efremenko [8]) we prove a
super-polynomial lower bound on the block-length of the
LDCs, assuming a well-known conjecture in additive
combinatorics, the polynomial Freiman-Ruzsa conjecture
over Z$_m$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ben-Sasson:2013:NFL,
author = "Eli Ben-Sasson and Ariel Gabizon and Yohay Kaplan and
Swastik Kopparty and Shubangi Saraf",
title = "A new family of locally correctable codes based on
degree-lifted algebraic geometry codes",
crossref = "ACM:2013:SPF",
pages = "833--842",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488714",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We describe new constructions of error correcting
codes, obtained by ``degree-lifting'' a short algebraic
geometry base-code of block-length $q$ to a lifted-code
of block-length $ q^m $, for arbitrary integer $m$. The
construction generalizes the way degree-d, univariate
polynomials evaluated over the $q$-element field (also
known as Reed--Solomon codes) are ``lifted'' to
degree-d, $m$-variate polynomials (Reed--Muller codes).
A number of properties are established: The rate of the
degree-lifted code is approximately a 1/m!-fraction of
the rate of the base-code. The relative distance of the
degree-lifted code is at least as large as that of the
base-code. This is proved using a generalization of the
Schwartz-Zippel Lemma to degree-lifted
Algebraic-Geometry codes. [Local correction] If the
base code is invariant under a group that is ``close''
to being doubly-transitive (in a precise manner defined
later) then the degree-lifted code is locally
correctable with query complexity at most $ q^2 $. The
automorphisms of the base-code are crucially used to
generate query-sets, abstracting the use of
affine-lines in the local correction procedure of
Reed--Muller codes. Taking a concrete illustrating
example, we show that degree-lifted Hermitian codes
form a family of locally correctable codes over an
alphabet that is significantly smaller than that
obtained by Reed--Muller codes of similar constant
rate, message length, and distance.",
acknowledgement = ack-nhfb,
}
@InProceedings{Guruswami:2013:LDR,
author = "Venkatesan Guruswami and Chaoping Xing",
title = "List decoding {Reed--Solomon}, algebraic-geometric,
and {Gabidulin} subcodes up to the singleton bound",
crossref = "ACM:2013:SPF",
pages = "843--852",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488715",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider Reed--Solomon (RS) codes whose evaluation
points belong to a subfield, and give a
linear-algebraic list decoding algorithm that can
correct a fraction of errors approaching the code
distance, while pinning down the candidate messages to
a well-structured affine space of dimension a constant
factor smaller than the code dimension. By pre-coding
the message polynomials into a subspace-evasive set, we
get a Monte Carlo construction of a subcode of
Reed--Solomon codes that can be list decoded from a
fraction $ (1 - R - \epsilon) $ of errors in polynomial
time (for any fixed $ \epsilon > 0 $) with a list size
of $ O(1 / \epsilon) $. Our methods extend to
algebraic-geometric (AG) codes, leading to a similar
claim over constant-sized alphabets. This matches
parameters of recent results based on folded variants
of RS and AG codes. but our construction here gives
subcodes of Reed--Solomon and AG codes themselves
(albeit with restrictions on the evaluation points).
Further, the underlying algebraic idea also extends
nicely to Gabidulin's construction of rank-metric codes
based on linearized polynomials. This gives the first
construction of positive rate rank-metric codes list
decodable beyond half the distance, and in fact gives
codes of rate $R$ list decodable up to the optimal $ (1
- R - \epsilon) $ fraction of rank errors. A similar
claim holds for the closely related subspace codes
studied by Koetter and Kschischang. We introduce a new
notion called subspace designs as another way to
pre-code messages and prune the subspace of candidate
solutions. Using these, we also get a deterministic
construction of a polynomial time list decodable
subcode of RS codes. By using a cascade of several
subspace designs, we extend our approach to AG codes,
which gives the first deterministic construction of an
algebraic code family of rate $R$ with efficient list
decoding from $ 1 - R - \epsilon $ fraction of errors
over an alphabet of constant size (that depends only on
$ \epsilon $). The list size bound is almost a
constant (governed by $ \log * $ (block length)), and
the code can be constructed in quasi-polynomial time.",
acknowledgement = ack-nhfb,
}
@InProceedings{Wootters:2013:LDR,
author = "Mary Wootters",
title = "On the list decodability of random linear codes with
large error rates",
crossref = "ACM:2013:SPF",
pages = "853--860",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488716",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "It is well known that a random $q$-ary code of rate $
\Omega (\epsilon^2) $ is list decodable up to radius $
(1 - 1 / q - \epsilon) $ with list sizes on the order
of $ 1 / \epsilon^2 $, with probability $ 1 - o(1) $.
However, until recently, a similar statement about
random linear codes has until remained elusive. In a
recent paper, Cheraghchi, Guruswami, and Velingker show
a connection between list decodability of random linear
codes and the Restricted Isometry Property from
compressed sensing, and use this connection to prove
that a random linear code of rate $ \Omega (\epsilon^2
/ \log^3 (1 / \epsilon)) $ achieves the list decoding
properties above, with constant probability. We improve
on their result to show that in fact we may take the
rate to be $ \Omega (\epsilon^2) $, which is optimal,
and further that the success probability is $ 1 - o(1)
$, rather than constant. As an added benefit, our proof
is relatively simple. Finally, we extend our methods to
more general ensembles of linear codes. As an example,
we show that randomly punctured Reed--Muller codes have
the same list decoding properties as the original
codes, even when the rate is improved to a constant.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brandao:2013:QFT,
author = "Fernando G. S. L. Brandao and Aram W. Harrow",
title = "Quantum {de Finetti} theorems under local measurements
with applications",
crossref = "ACM:2013:SPF",
pages = "861--870",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488718",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Quantum de Finetti theorems are a useful tool in the
study of correlations in quantum multipartite states.
In this paper we prove two new quantum de Finetti
theorems, both showing that under tests formed by local
measurements in each of the subsystems one can get a
much improved error dependence on the dimension of the
subsystems. We also obtain similar results for
non-signaling probability distributions. We give the
following applications of the results to quantum
complexity theory, polynomial optimization, and quantum
information theory: We prove the optimality of the
Chen-Drucker protocol for 3-SAT, under the assumption
there is no subexponential-time algorithm for SAT. In
the protocol a prover sends to a verifier $ \sqrt n
\polylog (n) $ unentangled quantum states, each
composed of $ O(\log (n)) $ qubits, as a proof of the
satisfiability of a 3-SAT instance with $n$ variables
and $ O(n) $ clauses. The quantum verifier checks the
validity of the proof by performing local measurements
on each of the proofs and classically processing the
outcomes. We show that any similar protocol with $
O(n^{1 / 2 - \epsilon }) $ qubits would imply a $ \exp
(n^{1 - 2 \epsilon } \polylog (n)) $-time algorithm for
3-SAT. We show that the maximum winning probability of
free games (in which the questions to each prover are
chosen independently) can be estimated by linear
programming in time $ \exp (O(\log |Q| + \log^2 |A| /
\epsilon^2)) $, with $ |Q| $ and $ |A| $ the question
and answer alphabet sizes, respectively, matching the
performance of a previously known algorithm due to
Aaronson, Impagliazzo, Moshkovitz, and Shor. This
result follows from a new monogamy relation for
non-locality, showing that $k$-extendible non-signaling
distributions give at most a $ O(k^{-1 / 2}) $
advantage over classical strategies for free games. We
also show that 3-SAT with $n$ variables can be reduced
to obtaining a constant error approximation of the
maximum winning probability under entangled strategies
of $ O(\sqrt n) $-player one-round non-local games, in
which only two players are selected to send $ O(\sqrt
n) $-bit messages. We show that the optimization of
certain polynomials over the complex hypersphere can be
performed in quasipolynomial time in the number of
variables $n$ by considering $ O(\log (n)) $ rounds of
the Sum-of-Squares (Parrilo/Lasserre) hierarchy of
semidefinite programs. This can be considered an
analogue to the hypersphere of a similar known results
for the simplex. As an application to entanglement
theory, we find a quasipolynomial-time algorithm for
deciding multipartite separability. We consider a
quantum tomography result due to Aaronson --- showing
that given an unknown $n$-qubit state one can perform
tomography that works well for most observables by
measuring only $ O(n) $ independent and identically
distributed (i.i.d.) copies of the state --- and relax
the assumption of having i.i.d copies of the state to
merely the ability to select subsystems at random from
a quantum multipartite state. The proofs of the new
quantum de Finetti theorems are based on information
theory, in particular on the chain rule of mutual
information. The results constitute improvements and
generalizations of a recent de Finetti theorem due to
Brandao, Christandl and Yard.",
acknowledgement = ack-nhfb,
}
@InProceedings{Brandao:2013:PSA,
author = "Fernando G. S. L. Brandao and Aram W. Harrow",
title = "Product-state approximations to quantum ground
states",
crossref = "ACM:2013:SPF",
pages = "871--880",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488719",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "The local Hamiltonian problem consists of estimating
the ground-state energy (given by the minimum
eigenvalue) of a local quantum Hamiltonian. It can be
considered as a quantum generalization of constraint
satisfaction problems (CSPs) and has a key role in
quantum complexity theory, being the first and most
natural QMA -complete problem known. An interesting
regime for the local Hamiltonian problem is that of
extensive error, where one is interested in estimating
the mean ground-state energy to constant accuracy. The
problem is NP -hard by the PCP theorem, but whether it
is QMA -hard is an important open question in quantum
complexity theory. A positive solution would represent
a quantum analogue of the PCP theorem. A key feature
that distinguishes quantum Hamiltonians from classical
CSPs is that the solutions may involve complicated
entangled states. In this paper, we demonstrate several
large classes of Hamiltonians for which product (i.e.
unentangled) states can approximate the ground state
energy to within a small extensive error. First, we
show the mere existence of a good product-state
approximation for the ground-state energy of 2-local
Hamiltonians with one of more of the following
properties: (1) super-constant degree, (2) small
expansion, or (3) a ground state with sublinear
entanglement with respect to some partition into small
pieces. The approximation based on degree is a new and
surprising difference between quantum Hamiltonians and
classical CSPs, since in the classical setting, higher
degree is usually associated with harder CSPs. The
approximation based on expansion is not new, but the
approximation based on low entanglement was previously
known only in the regime where the entanglement was
close to zero. Since the existence of a low-energy
product state can be checked in NP, this implies that
any Hamiltonian used for a quantum PCP theorem should
have: (1) constant degree, (2) constant expansion, (3)
a ``volume law'' for entanglement with respect to any
partition into small parts. Second, we show that in
several cases, good product-state approximations not
only exist, but can be found in deterministic
polynomial time: (1) 2-local Hamiltonians on any planar
graph, solving an open problem of Bansal, Bravyi, and
Terhal, (2) dense k -local Hamiltonians for any
constant k, solving an open problem of Gharibian and
Kempe, and (3) 2-local Hamiltonians on graphs with low
threshold rank, via a quantum generalization of a
recent result of Barak, Raghavendra and Steurer. Our
work involves two new tools which may be of independent
interest. First, we prove a new quantum version of the
de Finetti theorem which does not require the usual
assumption of symmetry. Second, we describe a way to
analyze the application of the Lasserre/Parrilo SDP
hierarchy to local quantum Hamiltonians.",
acknowledgement = ack-nhfb,
}
@InProceedings{Ta-Shma:2013:IWC,
author = "Amnon Ta-Shma",
title = "Inverting well conditioned matrices in quantum
logspace",
crossref = "ACM:2013:SPF",
pages = "881--890",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488720",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We show that quantum computers improve on the best
known classical algorithms for matrix inversion (and
singular value decomposition) as far as space is
concerned. This adds to the (still short) list of
important problems where quantum computers are of help.
Specifically, we show that the inverse of a well
conditioned matrix can be approximated in quantum
logspace with intermediate measurements. This should be
compared with the best known classical algorithm for
the problem that requires $ \Omega (\log^2 n) $ space.
We also show how to approximate the spectrum of a
normal matrix, or the singular values of an arbitrary
matrix, with $ \epsilon $ additive accuracy, and how to
approximate the singular value decomposition (SVD) of a
matrix whose singular values are well separated. The
technique builds on ideas from several previous works,
including simulating Hamiltonians in small quantum
space (building on [2] and [10]), treating a Hermitian
matrix as a Hamiltonian and running the quantum phase
estimation procedure on it (building on [5]) and making
small space probabilistic (and quantum) computation
consistent through the use of offline randomness and
the shift and truncate method (building on [8]).",
acknowledgement = ack-nhfb,
}
@InProceedings{Ambainis:2013:SAE,
author = "Andris Ambainis",
title = "Superlinear advantage for exact quantum algorithms",
crossref = "ACM:2013:SPF",
pages = "891--900",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488721",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "A quantum algorithm is exact if, on any input data, it
outputs the correct answer with certainty (probability
1). A key question is: how big is the advantage of
exact quantum algorithms over their classical
counterparts: deterministic algorithms. For total
Boolean functions in the query model, the biggest known
gap was just a factor of $2$: PARITY of $N$ input bits
requires $N$ queries classically but can be computed
with $ N / 2 $ queries by an exact quantum algorithm.
We present the first example of a Boolean function $
f(x_1, \ldots {}, x_N) $ for which exact quantum
algorithms have superlinear advantage over
deterministic algorithms. Any deterministic algorithm
that computes our function must use $N$ queries but an
exact quantum algorithm can compute it with $
O(N^{0.8675 \ldots }) $ queries. A modification of our
function gives a similar result for communication
complexity: there is a function f which can be computed
by an exact quantum protocol that communicates $
O(N^{0.8675 \ldots }) $ quantum bits but requires $
\Omega (N) $ bits of communication for classical
protocols.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2013:AKM,
author = "Shi Li and Ola Svensson",
title = "Approximating $k$-median via pseudo-approximation",
crossref = "ACM:2013:SPF",
pages = "901--910",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488723",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We present a novel approximation algorithm for
$k$-median that achieves an approximation guarantee of
$ 1 + \sqrt 3 + \epsilon $ , improving upon the
decade-old ratio of $ 3 + \epsilon $ . Our approach is
based on two components, each of which, we believe, is
of independent interest. First, we show that in order
to give an $ \alpha $ -approximation algorithm for
$k$-median, it is sufficient to give a
pseudo-approximation algorithm that finds an $ \alpha
$-approximate solution by opening $ k + O(1) $
facilities. This is a rather surprising result as there
exist instances for which opening $ k + 1 $ facilities
may lead to a significant smaller cost than if only $k$
facilities were opened. Second, we give such a
pseudo-approximation algorithm with $ \alpha = 1 +
\sqrt 3 + \epsilon $. Prior to our work, it was not
even known whether opening $ k + o(k) $ facilities
would help improve the approximation ratio.",
acknowledgement = ack-nhfb,
}
@InProceedings{Kelner:2013:SCA,
author = "Jonathan A. Kelner and Lorenzo Orecchia and Aaron
Sidford and Zeyuan Allen Zhu",
title = "A simple, combinatorial algorithm for solving {SDD}
systems in nearly-linear time",
crossref = "ACM:2013:SPF",
pages = "911--920",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488724",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In this paper, we present a simple combinatorial
algorithm that solves symmetric diagonally dominant
(SDD) linear systems in nearly-linear time. It uses
little of the machinery that previously appeared to be
necessary for a such an algorithm. It does not require
recursive preconditioning, spectral sparsification, or
even the Chebyshev Method or Conjugate Gradient. After
constructing a ``nice'' spanning tree of a graph
associated with the linear system, the entire algorithm
consists of the repeated application of a simple update
rule, which it implements using a lightweight data
structure. The algorithm is numerically stable and can
be implemented without the increased bit-precision
required by previous solvers. As such, the algorithm
has the fastest known running time under the standard
unit-cost RAM model. We hope the simplicity of the
algorithm and the insights yielded by its analysis will
be useful in both theory and practice.",
acknowledgement = ack-nhfb,
}
@InProceedings{Sherstov:2013:CLB,
author = "Alexander A. Sherstov",
title = "Communication lower bounds using directional
derivatives",
crossref = "ACM:2013:SPF",
pages = "921--930",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488725",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the set disjointness problem in the most
powerful bounded-error model: the
number-on-the-forehead model with $k$ parties and
arbitrary classical or quantum communication. We obtain
a communication lower bound of $ \Omega (\sqrt (n) /
2^k *k) $ bits, which is essentially optimal. Proving
it was a longstanding open problem even in restricted
settings, such as one-way classical protocols with $ k
= 4 $ parties (Wigderson 1997). The proof contributes a
novel technique for lower bounds on multiparty
communication, based on directional derivatives of
communication protocols over the reals.",
acknowledgement = ack-nhfb,
}
@InProceedings{Andoni:2013:HFU,
author = "Alexandr Andoni and Assaf Goldberger and Andrew
McGregor and Ely Porat",
title = "Homomorphic fingerprints under misalignments:
sketching edit and shift distances",
crossref = "ACM:2013:SPF",
pages = "931--940",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488726",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "Fingerprinting is a widely-used technique for
efficiently verifying that two files are identical.
More generally, linear sketching is a form of lossy
compression (based on random projections) that also
enables the ``dissimilarity'' of non-identical files to
be estimated. Many sketches have been proposed for
dissimilarity measures that decompose coordinate-wise
such as the Hamming distance between alphanumeric
strings, or the Euclidean distance between vectors.
However, virtually nothing is known on sketches that
would accommodate alignment errors. With such errors,
Hamming or Euclidean distances are rendered useless: a
small misalignment may result in a file that looks very
dissimilar to the original file according such
measures. In this paper, we present the first linear
sketch that is robust to a small number of alignment
errors. Specifically, the sketch can be used to
determine whether two files are within a small Hamming
distance of being a cyclic shift of each other.
Furthermore, the sketch is homomorphic with respect to
rotations: it is possible to construct the sketch of a
cyclic shift of a file given only the sketch of the
original file. The relevant dissimilarity measure,
known as the shift distance, arises in the context of
embedding edit distance and our result addressed an
open problem [Question 13 in
Indyk-McGregor-Newman-Onak'11] with a rather surprising
outcome. Our sketch projects a length $n$ file into $
D(n) \cdot \polylog n $ dimensions where $ D(n)l n $ is
the number of divisors of $n$. The striking fact is
that this is near-optimal, i.e., the $ D(n) $
dependence is inherent to a problem that is ostensibly
about lossy compression. In contrast, we then show that
any sketch for estimating the edit distance between two
files, even when small, requires sketches whose size is
nearly linear in $n$. This lower bound addresses a
long-standing open problem on the low distortion
embeddings of edit distance [Question 2.15 in
Naor-Matousek'11, Indyk'01], for the case of linear
embeddings.",
acknowledgement = ack-nhfb,
}
@InProceedings{Chonev:2013:OPH,
author = "Ventsislav Chonev and Jo{\"e}l Ouaknine and James
Worrell",
title = "The orbit problem in higher dimensions",
crossref = "ACM:2013:SPF",
pages = "941--950",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488728",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We consider higher-dimensional versions of Kannan and
Lipton's Orbit Problem---determining whether a target
vector space V may be reached from a starting point x
under repeated applications of a linear transformation
A. Answering two questions posed by Kannan and Lipton
in the 1980s, we show that when V has dimension one,
this problem is solvable in polynomial time, and when V
has dimension two or three, the problem is in
NP$^{RP}$.",
acknowledgement = ack-nhfb,
}
@InProceedings{Azar:2013:LSD,
author = "Yossi Azar and Ilan Reuven Cohen and Iftah Gamzu",
title = "The loss of serving in the dark",
crossref = "ACM:2013:SPF",
pages = "951--960",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488729",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study the following balls and bins stochastic
process: There is a buffer with B bins, and there is a
stream of balls X = {X$_1$, X$_2$, \ldots{} ,X$_T$ }
such that X$_i$ is the number of balls that arrive
before time i but after time i-1. Once a ball arrives,
it is stored in one of the unoccupied bins. If all the
bins are occupied then the ball is thrown away. In each
time step, we select a bin uniformly at random, clear
it, and gain its content. Once the stream of balls
ends, all the remaining balls in the buffer are cleared
and added to our gain. We are interested in analyzing
the expected gain of this randomized process with
respect to that of an optimal gain-maximizing strategy,
which gets the same online stream of balls, and clears
a ball from a bin, if exists, at any step. We name this
gain ratio the loss of serving in the dark. In this
paper, we determine the exact loss of serving in the
dark. We prove that the expected gain of the randomized
process is worse by a factor of $ \rho + \epsilon $
from that of the optimal gain-maximizing strategy for
any $ \epsilon > 0 $, where $ \rho = \max_{ \alpha > 1}
\alpha e^{ \alpha } / ((\alpha - 1)e^{ \alpha } + e -
1) \sim 1.69996 $ and $ B = \Omega (1 / \epsilon^3) $.
We also demonstrate that this bound is essentially
tight as there are specific ball streams for which the
above-mentioned gain ratio tends to $ \rho $. Our
stochastic process occurs naturally in many
applications. We present a prompt and truthful
mechanism for bounded capacity auctions, and an
application relating to packets scheduling.",
acknowledgement = ack-nhfb,
}
@InProceedings{Azar:2013:TBO,
author = "Yossi Azar and Ilan Reuven Cohen and Seny Kamara and
Bruce Shepherd",
title = "Tight bounds for online vector bin packing",
crossref = "ACM:2013:SPF",
pages = "961--970",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488730",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "In the $d$-dimensional bin packing problem (VBP), one
is given vectors $ x_1, x_2, \ldots {}, x_n \in R^d $
and the goal is to find a partition into a minimum
number of feasible sets: $ \{ 1, 2, \ldots {}, n \} =
\cup_i^s B_i $. A set $ B_i $ is feasible if $
\Sigma_{j \in B i} x_j \leq 1 $, where $1$ denotes the
all $1$'s vector. For online VBP, it has been
outstanding for almost 20 years to clarify the gap
between the best lower bound $ \Omega (1) $ on the
competitive ratio versus the best upper bound of $ O(d)
$. We settle this by describing a $ \Omega (d^{1 -
\epsilon }) $ lower bound. We also give strong lower
bounds (of $ \Omega (d^{1 / B - \epsilon }) $) if the
bin size $ B \in Z_+ $ is allowed to grow. Finally, we
discuss almost-matching upper bound results for general
values of $B$; we show an upper bound whose exponent is
additively ``shifted by 1'' from the lower bound
exponent.",
acknowledgement = ack-nhfb,
}
@InProceedings{Li:2013:SCO,
author = "Jian Li and Wen Yuan",
title = "Stochastic combinatorial optimization via {Poisson}
approximation",
crossref = "ACM:2013:SPF",
pages = "971--980",
year = "2013",
DOI = "https://doi.org/10.1145/2488608.2488731",
bibdate = "Mon Mar 3 06:30:33 MST 2014",
bibsource = "http://portal.acm.org/;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
abstract = "We study several stochastic combinatorial problems,
including the expected utility maximization problem,
the stochastic knapsack problem and the stochastic bin
packing problem. A common technical challenge in these
problems is to optimize some function (other than the
expectation) of the sum of a set of random variables.
The difficulty is mainly due to the fact that the
probability distribution of the sum is the convolution
of a set of distributions, which is not an easy
objective function to work with. To tackle this
difficulty, we introduce the Poisson approximation
technique. The technique is based on the Poisson
approximation theorem discovered by Le Cam, which
enables us to approximate the distribution of the sum
of a set of random variables using a compound Poisson
distribution. Using the technique, we can reduce a
variety of stochastic problems to the corresponding
deterministic multiple-objective problems, which either
can be solved by standard dynamic programming or have
known solutions in the literature. For the problems
mentioned above, we obtain the following results: We
first study the expected utility maximization problem
introduced recently [Li and Despande, FOCS11]. For
monotone and Lipschitz utility functions, we obtain an
additive PTAS if there is a multidimensional PTAS for
the multi-objective version of the problem, strictly
generalizing the previous result. The result implies
the first additive PTAS for maximizing threshold
probability for the stochastic versions of global
min-cut, matroid base and matroid intersection. For the
stochastic bin packing problem (introduced in
[Kleinberg, Rabani and Tardos, STOC97]), we show there
is a polynomial time algorithm which uses at most the
optimal number of bins, if we relax the size of each
bin and the overflow probability by e for any constant
$ \epsilon > 0 $. Based on this result, we obtain a
3-approximation if only the size of each bin can be
relaxed by $ \epsilon $ , improving the known $ O(1 /
\epsilon) $ factor for constant overflow probability.
For stochastic knapsack, we show a $ (1 + \epsilon)
$-approximation using $ \epsilon $ extra capacity for
any $ \epsilon > 0 $, even when the size and reward of
each item may be correlated and cancelations of items
are allowed. This generalizes the previous work
[Balghat, Goel and Khanna, SODA11] for the case without
correlation and cancelation. Our algorithm is also
simpler. We also present a factor $ 2 + \epsilon $
approximation algorithm for stochastic knapsack with
cancelations, for any constant $ \epsilon > 0 $,
improving the current known approximation factor of 8
[Gupta, Krishnaswamy, Molinaro and Ravi, FOCS11]. We
also study an interesting variant of the stochastic
knapsack problem, where the size and the profit of each
item are revealed before the decision is made. The
problem falls into the framework of Bayesian online
selection problems, which has been studied a lot
recently.",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2006:SPT,
editor = "{ACM}",
booktitle = "{STOC'06: Proceedings of the Thirty-Eighth Annual ACM
Symposium on Theory of Computing 2006, Seattle, WA,
USA, May 21--23, 2006}",
title = "{STOC'06: Proceedings of the Thirty-Eighth Annual ACM
Symposium on Theory of Computing 2006, Seattle, WA,
USA, May 21--23, 2006}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "770 (est.)",
year = "2006",
ISBN = "1-59593-134-1",
ISBN-13 = "978-1-59593-134-4",
LCCN = "QA75.5 .A22 2006",
bibdate = "Thu May 25 06:13:58 2006",
bibsource = "http://www.math.utah.edu/pub/tex/bib/stoc.bib;
http://www.math.utah.edu/pub/tex/bib/stoc2000.bib;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib;
z3950.gbv.de:20011/gvk",
note = "ACM order number 508060.",
URL = "http://portal.acm.org/citation.cfm?id=1132516",
acknowledgement = ack-nhfb,
}
@Proceedings{ACM:2010:SPA,
editor = "{ACM}",
booktitle = "{STOC'10: Proceedings of the 2010 ACM International
Symposium on Theory of Computing: June 5--8, 2010,
Cambridge, MA, USA}",
title = "{STOC'10: Proceedings of the 2010 ACM International
Symposium on Theory of Computing: June 5--8, 2010,
Cambridge, MA, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xiv + 797",
year = "2010",
ISBN = "1-60558-817-2",
ISBN-13 = "978-1-60558-817-9",
LCCN = "QA 76.6 .A152 2010",
bibdate = "Wed Sep 1 10:37:53 MDT 2010",
bibsource = "z3950.gbv.de:20011/gvk;
http://www.math.utah.edu/pub/tex/bib/stoc.bib;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
URL = "http://www.gbv.de/dms/tib-ub-hannover/63314455x.",
acknowledgement = ack-nhfb,
remark = "42nd annual STOC meeting.",
}
@Proceedings{ACM:2011:SPA,
editor = "{ACM}",
booktitle = "{STOC'11: Proceedings of the 2011 ACM International
Symposium on Theory of Computing: June 6--8, 2011, San
Jose, CA, USA}",
title = "{STOC'11: Proceedings of the 2011 ACM International
Symposium on Theory of Computing: June 6--8, 2011, San
Jose, CA, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "xxx + 822 (est.)",
year = "2011",
ISBN = "1-4503-0691-8",
ISBN-13 = "978-1-4503-0691-1",
LCCN = "????",
bibdate = "Wed Sep 1 10:37:53 MDT 2010",
bibsource = "z3950.gbv.de:20011/gvk;
http://www.math.utah.edu/pub/tex/bib/stoc.bib;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
URL = "http://www.gbv.de/dms/tib-ub-hannover/63314455x.",
acknowledgement = ack-nhfb,
remark = "43rd annual STOC meeting.",
}
@Proceedings{ACM:2012:SPA,
editor = "{ACM}",
booktitle = "{STOC'12: Proceedings of the 2012 ACM International
Symposium on Theory of Computing: May 19--22, 2012, New
York, NY, USA}",
title = "{STOC'12: Proceedings of the 2012 ACM International
Symposium on Theory of Computing: May 19--22, 2012, New
York, NY, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "1292 (est.)",
year = "2012",
ISBN = "1-4503-1245-4",
ISBN-13 = "978-1-4503-1245-5",
LCCN = "????",
bibdate = "Thu Nov 08 19:12:21 2012",
bibsource = "http://www.math.utah.edu/pub/tex/bib/stoc2010.bib;
http://www.math.utah.edu/pub/tex/bib/stoc.bib;
z3950.gbv.de:20011/gvk",
URL = "http://www.gbv.de/dms/tib-ub-hannover/63314455x.",
acknowledgement = ack-nhfb,
remark = "44th annual STOC meeting.",
}
@Proceedings{ACM:2013:SPF,
editor = "{ACM}",
booktitle = "{STOC '13: Proceedings of the Forty-fifth Annual ACM
Symposium on Theory of Computing: June 1--4, 2013, Palo
Alto, California, USA}",
title = "{STOC '13: Proceedings of the Forty-fifth Annual ACM
Symposium on Theory of Computing: June 1--4, 2013, Palo
Alto, California, USA}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "980 (est.)",
year = "2013",
ISBN = "1-4503-2029-5",
ISBN-13 = "978-1-4503-2029-0",
bibdate = "Mon Mar 3 06:36:05 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/datacompression.bib;
http://www.math.utah.edu/pub/tex/bib/prng.bib;
http://www.math.utah.edu/pub/tex/bib/stoc.bib;
http://www.math.utah.edu/pub/tex/bib/stoc2010.bib",
acknowledgement = ack-nhfb,
remark = "45th annual STOC meeting.",
}
