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Documents authored by Steurer, David

Document
DOI: 10.4230/LIPIcs.ITCS.2019.9
Small-Set Expansion in Shortcode Graph and the 2-to-2 Conjecture

Authors: Boaz Barak, Pravesh K. Kothari, and David Steurer

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
Dinur, Khot, Kindler, Minzer and Safra (2016) recently showed that the (imperfect completeness variant of) Khot's 2 to 2 games conjecture follows from a combinatorial hypothesis about the soundness of a certain "Grassmanian agreement tester". In this work, we show that soundness of Grassmannian agreement tester follows from a conjecture we call the "Shortcode Expansion Hypothesis" characterizing the non-expanding sets of the degree-two Short code graph. We also show the latter conjecture is equivalent to a characterization of the non-expanding sets in the Grassman graph, as hypothesized by a follow-up paper of Dinur et al. (2017). Following our work, Khot, Minzer and Safra (2018) proved the "Shortcode Expansion Hypothesis". Combining their proof with our result and the reduction of Dinur et al. (2016), completes the proof of the 2 to 2 conjecture with imperfect completeness. We believe that the Shortcode graph provides a useful view of both the hypothesis and the reduction, and might be suitable for obtaining new hardness reductions.
Cite as

Boaz Barak, Pravesh K. Kothari, and David Steurer. Small-Set Expansion in Shortcode Graph and the 2-to-2 Conjecture. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 9:1-9:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{barak_et_al:LIPIcs.ITCS.2019.9,
  author =	{Barak, Boaz and Kothari, Pravesh K. and Steurer, David},
  title =	{{Small-Set Expansion in Shortcode Graph and the 2-to-2 Conjecture}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{9:1--9:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.9},
  URN =		{urn:nbn:de:0030-drops-101022},
  doi =		{10.4230/LIPIcs.ITCS.2019.9},
  annote =	{Keywords: Unique Games Conjecture, Small-Set Expansion, Grassmann Graph, Shortcode}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018
LIPIcs, Volume 116, APPROX/RANDOM'18, Complete Volume

Authors: Eric Blais, Klaus Jansen, José D. P. Rolim, and David Steurer

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
LIPIcs, Volume 116, APPROX/RANDOM'18, Complete Volume
Cite as

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Proceedings{blais_et_al:LIPIcs.APPROX-RANDOM.2018,
  title =	{{LIPIcs, Volume 116, APPROX/RANDOM'18, Complete Volume}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018},
  URN =		{urn:nbn:de:0030-drops-97254},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018},
  annote =	{Keywords: Mathematics of computing, Theory of computation}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Eric Blais, Klaus Jansen, José D. P. Rolim, and David Steurer

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 0:i-0:xvi, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{blais_et_al:LIPIcs.APPROX-RANDOM.2018.0,
  author =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{0:i--0:xvi},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.0},
  URN =		{urn:nbn:de:0030-drops-94043},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.110
Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree

Authors: Boaz Barak, Ankur Moitra, Ryan O’Donnell, Prasad Raghavendra, Oded Regev, David Steurer, Luca Trevisan, Aravindan Vijayaraghavan, David Witmer, and John Wright

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Abstract
We show that for any odd k and any instance I of the max-kXOR constraint satisfaction problem, there is an efficient algorithm that finds an assignment satisfying at least a 1/2 + Omega(1/sqrt(D)) fraction of I's constraints, where D is a bound on the number of constraints that each variable occurs in. This improves both qualitatively and quantitatively on the recent work of Farhi, Goldstone, and Gutmann (2014), which gave a quantum algorithm to find an assignment satisfying a 1/2 Omega(D^{-3/4}) fraction of the equations. For arbitrary constraint satisfaction problems, we give a similar result for "triangle-free" instances; i.e., an efficient algorithm that finds an assignment satisfying at least a mu + Omega(1/sqrt(degree)) fraction of constraints, where mu is the fraction that would be satisfied by a uniformly random assignment.
Cite as

Boaz Barak, Ankur Moitra, Ryan O’Donnell, Prasad Raghavendra, Oded Regev, David Steurer, Luca Trevisan, Aravindan Vijayaraghavan, David Witmer, and John Wright. Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 110-123, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{barak_et_al:LIPIcs.APPROX-RANDOM.2015.110,
  author =	{Barak, Boaz and Moitra, Ankur and O’Donnell, Ryan and Raghavendra, Prasad and Regev, Oded and Steurer, David and Trevisan, Luca and Vijayaraghavan, Aravindan and Witmer, David and Wright, John},
  title =	{{Beating the Random Assignment on Constraint Satisfaction Problems of Bounded Degree}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{110--123},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.110},
  URN =		{urn:nbn:de:0030-drops-52981},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.110},
  annote =	{Keywords: constraint satisfaction problems, bounded degree, advantage over random}
}
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