How to Play Unique Games Using Embeddings

Authors:
Eden Chlamtac;Konstantin Makarychev;Yury Makarychev
Affiliations:
Princeton University, USA;Princeton University, USA;Princeton University, USA
Venue:
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Year:
2006

Citing 0
Cited 14

Vertex cuts, random walks, and dimension reduction in series-parallel graphs

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Parallel repetition in projection games and a concentration bound

STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Unique games on expanding constraint graphs are easy: extended abstract

STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Optimal algorithms and inapproximability results for every CSP?

STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Coarse Differentiation and Multi-flows in Planar Graphs

APPROX '07/RANDOM '07 Proceedings of the 10th International Workshop on Approximation and the 11th International Workshop on Randomization, and Combinatorial Optimization. Algorithms and Techniques
Partitioning graphs into balanced components

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Bilipschitz snowflakes and metrics of negative type

Proceedings of the forty-second ACM symposium on Theory of computing
Approximations for the isoperimetric and spectral profile of graphs and related parameters

Proceedings of the forty-second ACM symposium on Theory of computing
Genus and the geometry of the cut graph

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Fast SDP algorithms for constraint satisfaction problems

SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
How to play unique games on expanders

WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Unique Games with Entangled Provers Are Easy

SIAM Journal on Computing
Near-optimal distortion bounds for embedding doubling spaces into L1

Proceedings of the forty-third annual ACM symposium on Theory of computing
Parallel Repetition in Projection Games and a Concentration Bound

SIAM Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 - \varepsilon) fraction of all constraints is satisfiable, the algorithm finds an assignment satisfying a 1 - O\left( {\varepsilon \sqrt {\log n\log k} } \right) fraction of all constraints. To this end, we introduce new embedding techniques for rounding semidefinite relaxations of problems with large domain size.