Two prover protocols: low error at affordable rates
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
A new way of using semidefinite programming with applications to linear equations mod p
Journal of Algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
Randomized Rounding for Semidefinite Programs-Variations on the MAX CUT Example
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
On The Approximability Of The Traveling Salesman Problem
Combinatorica
On the (im)possibility of non-interactive correlation distillation
Theoretical Computer Science
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
An optimal sdp algorithm for max-cut, and equally optimal long code tests
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Conditional Hardness for Approximate Coloring
SIAM Journal on Computing
Composition of Low-Error 2-Query PCPs Using Decodable PCPs
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Approximating np-hard problems efficient algorithms and their limits
Approximating np-hard problems efficient algorithms and their limits
Two-query PCP with subconstant error
Journal of the ACM (JACM)
Spectral Algorithms for Unique Games
CCC '10 Proceedings of the 2010 IEEE 25th Annual Conference on Computational Complexity
Subexponential Algorithms for Unique Games and Related Problems
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Hardness of Max-2Lin and Max-3Lin over Integers, Reals, and Large Cyclic Groups
CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Rounding Semidefinite Programming Hierarchies via Global Correlation
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Approximation resistance from pairwise independent subgroups
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Approximation resistance on satisfiable instances for predicates with few accepting inputs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
New NP-Hardness Results for 3-Coloring and 2-to-1 Label Cover
ACM Transactions on Computation Theory (TOCT)
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We show that distinguishing 1/2-satisfiable Unique-Games instances from (3/8 + ε)-satisfiable instances is NP-hard (for all ε 0). A consequence is that we match or improve the best known c vs. s NP-hardness result for Unique-Games for all values of c (except for c very close to 0). For these c, ours is the first hardness result showing that it helps to take the alphabet size larger than 2. Our NP-hardness reductions are quasilinear-size and thus show nearly full exponential time is required, assuming the ETH.