Candidate hard unique game

Subhash Khot, Dana Moshkovitz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We propose a candidate reduction for ruling out polynomialtime algorithms for unique games, either under plausible complexity assumptions, or unconditionally for Lasserre semidefinite programs with a constant number of rounds. We analyze the completeness and Lasserre solution of our construction, and provide a soundness analysis in a certain setting of interest. Addressing general settings is tightly connected to a question on Gaussian isoperimetry. Our construction is based on our previous work on the complexity of approximately solving a system of linear equations over reals, which we suggested as an avenue towards a (positive) resolution of the Unique Games Conjecture. The construction employs a new encoding scheme based on half-spaces that we call the real code. The real code has two useful properties: like the long code, it has a unique local test, and like the Hadamard code, it has the so-called sub-code covering property.

Original languageEnglish (US)
Title of host publicationSTOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing
PublisherAssociation for Computing Machinery
Pages63-76
Number of pages14
Volume19-21-June-2016
ISBN (Electronic)9781450341325
DOIs
StatePublished - Jun 19 2016
Event48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016 - Cambridge, United States
Duration: Jun 19 2016Jun 21 2016

Other

Other48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016
CountryUnited States
CityCambridge
Period6/19/166/21/16

Fingerprint

Linear equations

Keywords

  • Approximate real linear equations
  • Direct product theorem
  • Gaussian isoperimetry
  • Half-space
  • Integrality gap
  • Lasserre hierarchy
  • Leakage
  • Probabilistically checkable proofs (PCP)
  • Real code
  • Semidefinite programming (SDP)
  • Two prover games
  • Unique games conjecture (UGC)

ASJC Scopus subject areas

  • Software

Cite this

Khot, S., & Moshkovitz, D. (2016). Candidate hard unique game. In STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing (Vol. 19-21-June-2016, pp. 63-76). Association for Computing Machinery. https://doi.org/10.1145/2897518.2897531

Candidate hard unique game. / Khot, Subhash; Moshkovitz, Dana.

STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing. Vol. 19-21-June-2016 Association for Computing Machinery, 2016. p. 63-76.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Khot, S & Moshkovitz, D 2016, Candidate hard unique game. in STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing. vol. 19-21-June-2016, Association for Computing Machinery, pp. 63-76, 48th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2016, Cambridge, United States, 6/19/16. https://doi.org/10.1145/2897518.2897531
Khot S, Moshkovitz D. Candidate hard unique game. In STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing. Vol. 19-21-June-2016. Association for Computing Machinery. 2016. p. 63-76 https://doi.org/10.1145/2897518.2897531
Khot, Subhash ; Moshkovitz, Dana. / Candidate hard unique game. STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing. Vol. 19-21-June-2016 Association for Computing Machinery, 2016. pp. 63-76
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