research-article

Candidate hard unique game

Authors:

Dana MoshkovitzAuthors Info & Claims

STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

Pages 63 - 76

https://doi.org/10.1145/2897518.2897531

Published: 19 June 2016 Publication History

Abstract

We propose a candidate reduction for ruling out polynomial-time algorithms for unique games, either under plausible complexity assumptions, or unconditionally for Lasserre semi-definite 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 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.

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Cited By

Heilman S(2019)A periodic isoperimetric problem related to the unique games conjectureRandom Structures & Algorithms10.1002/rsa.2087756:1(154-168)Online publication date: 24-Jul-2019
https://doi.org/10.1002/rsa.20877
Mossel ENeeman J(2018)Noise stability and correlation with half spacesElectronic Journal of Probability10.1214/18-EJP14523:noneOnline publication date: 1-Jan-2018
https://doi.org/10.1214/18-EJP145
Dinur IKhot SKindler GMinzer DSafra MDiakonikolas IKempe DHenzinger M(2018)Towards a proof of the 2-to-1 games conjecture?Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188804(376-389)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188804
Show More Cited By

Candidate hard unique game
1. Theory of computation

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cover image ACM Conferences

STOC '16: Proceedings of the forty-eighth annual ACM symposium on Theory of Computing

June 2016

1141 pages

ISBN:9781450341325

DOI:10.1145/2897518

General Chair:
Daniel Wichs
Northeastern, USA
,
Program Chair:
Yishay Mansour
Tel Aviv

Copyright © 2016 ACM.

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Published: 19 June 2016

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June 19 - 21, 2016

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Cited By

Heilman S(2019)A periodic isoperimetric problem related to the unique games conjectureRandom Structures & Algorithms10.1002/rsa.2087756:1(154-168)Online publication date: 24-Jul-2019
https://doi.org/10.1002/rsa.20877
Mossel ENeeman J(2018)Noise stability and correlation with half spacesElectronic Journal of Probability10.1214/18-EJP14523:noneOnline publication date: 1-Jan-2018
https://doi.org/10.1214/18-EJP145
Dinur IKhot SKindler GMinzer DSafra MDiakonikolas IKempe DHenzinger M(2018)Towards a proof of the 2-to-1 games conjecture?Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3188745.3188804(376-389)Online publication date: 20-Jun-2018
https://dl.acm.org/doi/10.1145/3188745.3188804
Subhash KMinzer DSafra M(2018)Pseudorandom Sets in Grassmann Graph Have Near-Perfect Expansion2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS.2018.00062(592-601)Online publication date: Oct-2018
https://doi.org/10.1109/FOCS.2018.00062
Kothari PMori RO'Donnell RWitmer DHatami HMcKenzie PKing V(2017)Sum of squares lower bounds for refuting any CSPProceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing10.1145/3055399.3055485(132-145)Online publication date: 19-Jun-2017
https://dl.acm.org/doi/10.1145/3055399.3055485

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