Randomized algorithms
Approximation algorithms for NP-hard problems
Approximation algorithms for NP-hard problems
On Semidefinite Programming Relaxations of (2+p)-SAT
Annals of Mathematics and Artificial Intelligence
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)
Mick gets some (the odds are on his side) (satisfiability)
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
MaxSolver: An efficient exact algorithm for (weighted) maximum satisfiability
Artificial Intelligence
k-Clustering Minimum Biclique Completion via a Hybrid CP and SDP Approach
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The accuracy of search heuristics: an empirical study on knapsack problems
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Alternating control tree search for knapsack/covering problems
Journal of Heuristics
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Recently, Linear Programming (LP)-based relaxations have been shown promising in boosting the performance of exact MAX-SAT solvers. We compare Semidefinite Programming (SDP) based relaxations with LP relaxations for MAX-2-SAT. We will show how SDP relaxations are surprisingly powerful, providing much tighter bounds than LP relaxations, across different constrainedness regions. SDP relaxations can also be computed very efficiently, thus quickly providing tight lower and upper bounds on the optimal solution. We also show the effectiveness of SDP relaxations in providing heuristic guidance for iterative variable setting, significantly more accurate than the guidance based on LP relaxations. SDP allows us to set up to around 80% of the variables without degrading the optimal solution, while setting a single variable based on the LP relaxation generally degrades the global optimal solution in the overconstrained area. Our results therefore show that SDP relaxations may further boost exact MAX-SAT solvers.