Survey Propagation Revisited

Survey propagation (SP) is an exciting new technique that has been remarkably successful at solving very large hard combinatorial problems, such as determining the satisfiability of Boolean formulas. In a promising attempt at understanding the success of SP, it was recently shown that SP can be viewed as a form of belief propagation, computing marginal probabilities over certain objects called covers of a formula. This explanation was, however, shortly dismissed by experiments suggesting that non-trivial covers simply do not exist for large formulas. In this paper, we show that these experiments were misleading: not only do covers exist for large hard random formulas, SP is surprisingly accurate at computing marginals over these covers despite the existence of many cycles in the formulas. This re-opens a potentially simpler line of reasoning for understanding SP, in contrast to some alternative lines of explanation that have been proposed assuming covers do not exist.