Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Gadgets, Approximation, and Linear Programming
SIAM Journal on 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 algorithms for MAX 4-SAT and rounding procedures for semidefinite programs
Journal of Algorithms
An Interior Proximal Algorithm and the Exponential Multiplier Method for Semidefinite Programming
SIAM Journal on Optimization
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
63-Approximation Algorithm for MAX DICUT
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
Journal of Computer and System Sciences - STOC 2001
Maximizing Quadratic Programs: Extending Grothendieck's Inequality
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Matrix Exponentiated Gradient Updates for On-line Learning and Bregman Projection
The Journal of Machine Learning Research
Near-optimal algorithms for unique games
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
How to Play Unique Games Using Embeddings
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
A combinatorial, primal-dual approach to semidefinite programs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Near-optimal algorithms for maximum constraint satisfaction problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Max cut and the smallest eigenvalue
Proceedings of the forty-first annual ACM symposium on Theory of computing
COLT'06 Proceedings of the 19th annual conference on Learning Theory
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Strong converse for identification via quantum channels
IEEE Transactions on Information Theory
Mirror descent and nonlinear projected subgradient methods for convex optimization
Operations Research Letters
Subsampling mathematical relaxations and average-case complexity
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
| Hi-index | 0.02 |
The class of constraint satisfactions problems (CSPs) captures many fundamental combinatorial optimization problems such as Max Cut, Max q-Cut, Unique Games, and Max k-Sat. Recently, Raghavendra (STOC'08) identified a simple semidefinite programming relaxation that gives the best possible approximation for any CSP, assuming the Unique Games Conjecture. Raghavendra and Steurer (FOCS'09) showed that, independent of the truth of the Unique Games Conjecture, the integrality gap of this relaxation cannot be improved even by adding a large class of valid inequalities. We present an algorithm that finds an approximately optimal solution to this relaxation in near-linear time. Combining this algorithm with a rounding scheme of Raghavendra and Steurer (FOCS'09) leads to an approximation algorithm for any CSP that runs in near-linear time and has an approximation guarantee that matches the integrality gap, which is optimal assuming the Unique Games Conjecture.