Approximation algorithms
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
O(√log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Near-optimal algorithms for unique games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Conditional hardness for approximate coloring
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Approximating maximum satisfiable subsystems of linear equations of bounded width
Information Processing Letters
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
Linear time approximation schemes for the Gale-Berlekamp game and related minimization problems
Proceedings of the forty-first annual ACM symposium on Theory of computing
ACM Transactions on Computation Theory (TOCT)
FPT algorithms for path-transversals and cycle-transversals problems in graphs
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Approximate Lasserre integrality gap for unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Improving integrality gaps via Chvátal-Gomory rounding
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
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
FPT algorithms for path-transversal and cycle-transversal problems
Discrete Optimization
Parallel Repetition in Projection Games and a Concentration Bound
SIAM Journal on Computing
Column Subset Selection Problem is UG-hard
Journal of Computer and System Sciences
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The UNIQUE GAMES problem is the following: we are given a graph G = (V, E), with each edge e = (u, v) having a weight we and a permutation πuv on [k]. The objective is to find a labeling of each vertex u with a label fu ∈ [k] to minimize the weight of unsatisfied edges---where an edge (u, v) is satisfied if fv = πuv(fu).The Unique Games Conjecture of Khot [8] essentially says that for each ε 0, there is a k such that it is NP-hard to distinguish instances of Unique games with (1-ε) satisfiable edges from those with only ε satisfiable edges. Several hardness results have recently been proved based on this assumption, including optimal ones for Max-Cut, Vertex-Cover and other problems, making it an important challenge to prove or refute the conjecture.In this paper, we give an O(log n)-approximation algorithm for the problem of minimizing the number of unsatisfied edges in any Unique game. Previous results of Khot [8] and Trevisan [12] imply that if the optimal solution has OPT = εm unsatisfied edges, semidefinite relaxations of the problem could give labelings with min {k2ε1/5, (ε log n)1/2}m unsatisfied edges. In this paper we show how to round a LP relaxation to get an O(log n)-approximation to the problem; i.e., to find a labeling with only O(εm log n) = O(OPT log n) unsatisfied edges.