Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Rounding Techniques for the MAX 2-SAT and MAX DI-CUT Problems
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Maximizing Quadratic Programs: Extending Grothendieck's Inequality
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Approximating Max kCSP - outperforming a random assignment with almost a linear factor
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Conditional Hardness of Approximating Satisfiable Max 3CSP-q
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Fast SDP algorithms for constraint satisfaction problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
A lower bound on the value of entangled binary games
Quantum Information & Computation
Approximating CSPs with global cardinality constraints using SDP hierarchies
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Complexity of approximating CSP with balance / hard constraints
Proceedings of the 5th conference on Innovations in theoretical computer science
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In this paper we present approximation algorithms for the maximum constraint satisfaction problem with k variables in each constraint (MAX k-CSP). Given a (1 - ε) satisfiable 2CSP our first algorithm finds an assignment of variables satisfying a 1 - O(√ε) fraction of all constraints. The best previously known result, due to Zwick, was 1 - O(ε1/3). The second algorithm finds a ck/2k approximation for the MAX k-CSP problem (where c 0.44 is an absolute constant). This result improves the previously best known algorithm by Hast, which had an approximation guarantee of Ω(k/(2klog k)). Both results are optimal assuming the Unique Games Conjecture and are based on rounding natural semidefinite programming relaxations. We also believe that our algorithms and their analysis are simpler than those previously known.