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Abstract

Constraint Satisfaction Problems (CSPs) are defined over a set of variables whose state must satisfy a number of constraints. We study a class of algorithms called Message Passing Algorithms, which aim at finding the probability distribution of the variables over the space of satisfying assignments. These algorithms involve passing local messages (according to some message update rules) over the edges of a factor graph constructed corresponding to the CSP. We focus on the Belief Propagation (BP) algorithm, which finds exact solution marginals for tree-like factor graphs. However, convergence and exactness cannot be guaranteed for a general factor graph. We propose a method for improving BP to account for cycles in the factor graph. We also study another message passing algorithm known as Survey Propagation (SP), which is empirically quite effective in solving random K-SAT instances, even when the density is close to the satisfiability threshold. We contribute to the theoretical understanding of SP by deriving the SP equations from the BP message update rules.