Backbone variables have the same assignment in all solutions to a given constraint satisfaction problem; more generally, bias represents the proportion of solutions that assign a variable a particular value. Intuitively such constructs would seem important to efficient search, but their study to date has been from a mostly conceptual perspective, in terms of indicating problem hardness or motivating and interpreting heuristics. Here we summarize a two-phase project where we first measure the ability of both existing and novel probabilistic message-passing techniques to directly estimate bias and identify backbones for the Boolean Satisfiability (SAT) Problem. We confirm that methods like Belief Propagation and Survey Propagation
Eric I. Hsu, Christian J. Muise, J. Christopher Be