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On the unique games conjecture
 In FOCS
, 2005
"... This article surveys recently discovered connections between the Unique Games Conjecture and computational complexity, algorithms, discrete Fourier analysis, and geometry. 1 ..."
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Cited by 15 (1 self)
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This article surveys recently discovered connections between the Unique Games Conjecture and computational complexity, algorithms, discrete Fourier analysis, and geometry. 1
Approximation algorithms for unique games
 In FOCS ’05: Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
"... Abstract: A unique game is a type of constraint satisfaction problem with two variables per constraint. The value of a unique game is the fraction of the constraints satisfied by an optimal solution. Khot (STOC’02) conjectured that for arbitrarily small γ,ε> 0 it is NPhard to distinguish games of ..."
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Cited by 46 (0 self)
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Abstract: A unique game is a type of constraint satisfaction problem with two variables per constraint. The value of a unique game is the fraction of the constraints satisfied by an optimal solution. Khot (STOC’02) conjectured that for arbitrarily small γ,ε> 0 it is NPhard to distinguish games
SPECTRAL ALGORITHMS FOR UNIQUE Games
"... We give a new algorithm for Unique Games which is based on purely spectral techniques, in contrast to previous work in the area, which relies heavily on semidefinite programming (SDP). Given a highly satisfiable instance of Unique Games, our algorithm is able to recover a good assignment. The appro ..."
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Cited by 17 (1 self)
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We give a new algorithm for Unique Games which is based on purely spectral techniques, in contrast to previous work in the area, which relies heavily on semidefinite programming (SDP). Given a highly satisfiable instance of Unique Games, our algorithm is able to recover a good assignment
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 ..."
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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
Unique Games Over Integers
"... Consider systems of twovariable linear equations of the form xi−xj = cij, where the cij’s are integer constants. We show that even if there is an integer solution satisfying at least a (1 − ɛ)fraction of the equations, it is UniqueGameshard to find an integer (or even real) solution satisfying at ..."
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Consider systems of twovariable linear equations of the form xi−xj = cij, where the cij’s are integer constants. We show that even if there is an integer solution satisfying at least a (1 − ɛ)fraction of the equations, it is UniqueGameshard to find an integer (or even real) solution satisfying
Unique Games on the Hypercube
, 2014
"... In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the GoemansWilliamson semidefinite program (SDP) for Max2LIN(Z2). We conjecture that adding tr ..."
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In this paper, we investigate the validity of the Unique Games Conjecture when the constraint graph is the boolean hypercube. We construct an almost optimal integrality gap instance on the Hypercube for the GoemansWilliamson semidefinite program (SDP) for Max2LIN(Z2). We conjecture that adding
Approximating unique games
 In Proc. SODA’06
, 2006
"... 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 satisf ..."
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Cited by 24 (1 self)
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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
Approximation Algorithms for Unique Games
, 2005
"... 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 ..."
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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
Nearoptimal algorithms for Unique Games
 In Proceedings of the 38th Annual ACM Symposium on Theory of Computing
, 2006
"... Unique games are constraint satisfaction problems that can be viewed as a generalization of MaxCut 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 ar ..."
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Cited by 47 (8 self)
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Unique games are constraint satisfaction problems that can be viewed as a generalization of MaxCut 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
On the Complexity of Unique Games and Graph Expansion
"... Understanding the complexity of approximating basic optimization problems is one of the grand challenges of theoretical computer science. In recent years, a sequence of works established that Khot’s Unique Games Conjecture, if true, would settle the approximability of many of these problems, making ..."
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Cited by 3 (0 self)
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Understanding the complexity of approximating basic optimization problems is one of the grand challenges of theoretical computer science. In recent years, a sequence of works established that Khot’s Unique Games Conjecture, if true, would settle the approximability of many of these problems, making
Results 1  10
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310,743