Approximation Algorithms for Unique Games

We present a polynomial time algorithm based on semidefinite programming that, given a unique game of value 1 − O(1/ log n), satisfies a constant fraction of constraints, where n is the number of variables. For sufficiently large alphabets, it improves an algorithm of Khot (STOC’02) that satisfies a constant fraction of constraints in unique games of value 1 − c/(k10 (log k)5 ), where k is the size of the alphabet. We also present a simpler algorithm for the special case of unique games with linear constraints, and a combinatorial algorithm for the general case. Finally, we present a simple approximation algorithm for 2-to-1 games.

• Type: Conference
• Year: 2005
• Where: FOCS
• Authors: Luca Trevisan
• Keywords: Algorithm, Constant Fraction, FOCS 2005, Theoretical Computer Science, Unique Games