Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Survey propagation: An algorithm for satisfiability
Random Structures & Algorithms
Detecting disjoint inconsistent subformulas for computing lower bounds for Max-SAT
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Existential arc consistency: getting closer to full arc consistency in weighted CSPs
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Three truth values for the SAT and Max-SAT problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
UBCSAT: an implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT
SAT'04 Proceedings of the 7th international conference on Theory and Applications of Satisfiability Testing
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Relaxed survey propagation for the weighted maximum satisfiability problem
Journal of Artificial Intelligence Research
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The survey propagation (SP) algorithm has been shown to work well on large instances of the random 3-SAT problem near its phase transition. It was shown that SP estimates marginals over covers, using joker states to represent clusters of configurations. The SP-y algorithm generalizes SP to work on the Max-SAT problem, but the cover interpretation of SP does not generalize to SP-y. Recently, a relaxed survey propagation (RSP) algorithm has been proposed for inference in Markov random fields (MRF). RSP for MRFs assigns zero probability to joker states, and hence the cover interpretation is also inapplicable. We adapt RSP to solve Max-SAT problems, and show that it has an interpretation of estimating marginals over covers violating a minimum number of clauses. This naturally generalizes the cover interpretation of SP. Empirically, we show that RSP out-performs SP-y and other state-of-the-art solvers on random as well as benchmark instances of Max-SAT.