How to Play Unique Games Using Embeddings

@article{Chlamtc2006HowTP,
  title={How to Play Unique Games Using Embeddings},
  author={Eden Chlamt{\'a}c and Konstantin Makarychev and Yury Makarychev},
  journal={2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)},
  year={2006},
  pages={687-696}
}
In this paper we present a new approximation algorithm for unique games. For a unique game with n vertices and k states (labels), if a (1 - epsiv) fraction of all constraints is satisfiable, the algorithm finds an assignment satisfying a 1 - O(epsiv radic(log n log k)) fraction of all constraints. To this end, we introduce new embedding techniques for rounding semidefinite relaxations of problems with large domain size 
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