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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 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 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)

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)

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)

- Ryan Williams, Carla P. Gomes, Bart Selman
- IJCAI
- 2003

There has been significant recent progress in reasoning and constraint processing methods. In areas such as planning and finite model-checking, current solution techniques can handle combinatorial problems with up to a million variables and five million constraints. The good scaling behavior of these methods appears to defy what one would expect based on a… (More)

Recent progress on search and reasoning procedures has been driven by experimentation on computation-ally hard problem instances. Hard random problem distributions are an important source of such instances. Challenge problems from the area of nite algebra have also stimulated research on search and reasoning procedures. Nevertheless, the relation of such… (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)

We consider the problem of sampling from a probability distribution defined over a high-dimensional discrete set, specified for instance by a graphical model. We propose a sampling algorithm, called PAWS, based on embedding the set into a higher-dimensional space which is then randomly projected using universal hash functions to a lower-dimensional subspace… (More)