Candidate hard unique game

Subhash Khot, Dana Moshkovitz
2016 Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016  
We propose a candidate reduction for ruling out polynomial-time 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 a suggestion in
more » ... [30] wherein the authors study the complexity of approximately solving a system of linear equations over reals and suggest it 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. * A preliminary version of this paper without a soundness analysis appeared as ECCC TR14-142.
doi:10.1145/2897518.2897531 dblp:conf/stoc/KhotM16 fatcat:urhpe5lwqfagpdrxotjgdbh5wu