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-plus Expectation Maximization-based variants-do produce good estimates with distinctive properties. The second phase demonstrates the use of bias estimation within a modern SAT solver, exhibiting a correlation between accurate, stable, estimates and successful backtracking search. The same process also yields a family of search heuristics that can dramatically improve search efficiency for the hard random problems considered. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Hsu, E. I., Muise, C. J., Beck, J. C., & McIlraith, S. A. (2008). Probabilistically estimating backbones and variable bias: Experimental overview. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5202 LNCS, pp. 613–617). https://doi.org/10.1007/978-3-540-85958-1_52
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