Relaxed survey propagation: A sum-product algorithm for max-SAT

Abstract

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 outperforms SP-y and other state-of-the-art solvers on random as well as benchmark instances of Max-SAT. Copyright © 2008, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved.