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). 

• Type: Conference
• Year: 2010
• Where: APPROX
• Authors: Subhash Khot, Preyas Popat, Rishi Saket
• Keywords: Algorithms, APPROX 2010, Lasserre SDP Relaxation, Unique Games, UNIQUE GAMES Problem