A new look at survey propagation and its generalizations

This article provides a new conceptual perspective on survey propagation, which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k-SAT problems even with densities close to the satisfiability threshold. We first describe how any SAT formula can be associated with a novel family of Markov random fields (MRFs), parameterized by a real number ρ ∈ [0, 1]. We then show that applying belief propagation—a wellknown “message-passing” technique for estimating marginal probabilities—to this family of MRFs recovers a known family of algorithms, ranging from pure survey propagation at one extreme (ρ = 1) to standard belief propagation on the uniform distribution over SAT assignments at the other extreme (ρ = 0). Configurations in these MRFs have a natural interpretation as partial satisfiability assignments, on which a partial order can be defined. We isolate cores as minimal elements in this partial orde...

• Type: Journal
• Year: 2007
• Where: JACM
• Authors: Elitza N. Maneva, Elchanan Mossel, Martin J. Wainwright
• Keywords: JACM 2007, Random K-SAT Problems, Statistical Physics Community, Survey Propagation