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2006
ACM

Near-optimal algorithms for unique games

14 years 3 months ago
Near-optimal algorithms for unique games
Unique games are constraint satisfaction problems that can be viewed as a generalization of Max-Cut to a larger domain size. The Unique Games Conjecture states that it is hard to distinguish between instances of unique games where almost all constraints are satisfiable and those where almost none are satisfiable. It has been shown to imply a number of inapproximability results for fundamental problems that seem difficult to obtain by more standard complexity assumptions. Thus, proving or refuting this conjecture is an important goal. We present significantly improved approximation algorithms for unique games. For instances with domain size k where the optimal solution satisfies 1 - fraction of all constraints, our algorithms satisfy roughly k-/(2-) and 1 - O( log k) fraction of all constraints. Our algorithms are based on rounding a natural semidefinite programming relaxation for the problem and their performance almost matches the integrality gap of this relaxation. Our results are...
Moses Charikar, Konstantin Makarychev, Yury Makary
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2006
Where STOC
Authors Moses Charikar, Konstantin Makarychev, Yury Makarychev
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