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Unpredictability in the running time of complete search procedures can often be explained by the phenomenon of " heavy-tailed cost distributions " , meaning that at any time during the experiment there is a non-negligible probability of hitting a problem that requires exponentially more time to solve than any that has been encountered before (Gomes et al.(More)
We introduce a new technique for counting models of Boolean satisfiability problems. Our approach incorporates information obtained from sampling the solution space. Unlike previous approaches, our method does not require uniform or near-uniform samples. It instead converts local search sampling without any guarantees into very good bounds on the model(More)
We study the runtime distributions of backtrack procedures for propositional satisfiability and constraint satisfaction. Such procedures often exhibit a large variability in performance. Our study reveals some intriguing properties of such distributions: They are often characterized by very long tails or " heavy tails ". We will show that these(More)
We propose a new technique for sampling the solutions of combinatorial problems in a near-uniform manner. We focus on problems specified as a Boolean formula , i.e., on SAT instances. Sampling for SAT problems has been shown to have interesting connections with probabilistic reasoning, making practical sampling algorithms for SAT highly desirable. The best(More)
A major difficulty in evaluating incomplete local search style algorithms for constraint satisfaction problems is the need for a source of hard problem instances that are guaranteed to be satisfiable. A standard approach to evaluate incomplete search methods has been to use a general problem generator and a complete search method to filter out the(More)
The past few years have seen an enormous progress in the performance of Boolean satisfiability (SAT) solvers. Despite the worst-case exponential run time of all known algorithms, satisfiability solvers are increasingly leaving their mark as a general-purpose tool in areas as diverse as software and hardware verification [29–31, 228], automatic test pattern(More)
We describe research and results centering on the construction and use of Bayesian models that can predict the run time of problem solvers. Our efforts are motivated by observations of high variance in the time required to solve instances for several challenging problems. The methods have application to the decision-theoretic control of hard search and(More)