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APPROX
2010
Springer

Approximate Lasserre Integrality Gap for Unique Games

13 years 5 months ago
Approximate Lasserre Integrality Gap for Unique Games
In this paper, we investigate whether a constant round Lasserre Semi-definite Programming (SDP) relaxation might give a good approximation to the UNIQUE GAMES problem. We show that the answer is negative if the relaxation is insensitive to a sufficiently small perturbation of the constraints. Specifically, we construct an instance of UNIQUE GAMES with k labels along with an approximate vector solution to t rounds of the Lasserre SDP relaxation. The SDP objective is at least 1- whereas the integral optimum is at most , and all SDP constraints are satisfied up to an accuracy of > 0. Here , > 0 and t Z+ are arbitrary constants and k = k(, ) Z+ . The accuracy parameter can be made sufficiently small independent of parameters , , t, k (but the size of the instance grows as gets smaller).
Subhash Khot, Preyas Popat, Rishi Saket
Added 26 Oct 2010
Updated 26 Oct 2010
Type Conference
Year 2010
Where APPROX
Authors Subhash Khot, Preyas Popat, Rishi Saket
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