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
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
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Towards Sharp Inapproximability For Any 2-CSP
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Approximation Resistant Predicates from Pairwise Independence
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
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
Black-box reductions in mechanism design
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Tight bounds on the approximability of almost-satisfiable Horn SAT and exact hitting set
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Robust satisfiability of constraint satisfaction problems
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Approximation resistance from pairwise independent subgroups
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Robust Satisfiability for CSPs: Hardness and Algorithmic Results
ACM Transactions on Computation Theory (TOCT)
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In this article, we present two 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(&sqrt;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/(2k log 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.