Monte-Carlo approximation algorithms for enumeration problems
Journal of Algorithms
Counting the number of solutions for instances of satisfiability
Theoretical Computer Science
Randomized algorithms
Number of models and satisfiability of sets of clauses
Theoretical Computer Science
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
A Probabilistic 3-SAT Algorithm Further Improved
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
An improved exponential-time algorithm for k-SAT
Journal of the ACM (JACM)
Randomized Algorithms for 3-SAT
Theory of Computing Systems
New upper bound for the #3-SAT problem
Information Processing Letters
A tighter bound for counting max-weight solutions to 2SAT instances
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
A full derandomization of schöning's k-SAT algorithm
Proceedings of the forty-third annual ACM symposium on Theory of computing
Derandomizing HSSW algorithm for 3-SAT
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
A satisfiability algorithm for AC0
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We present an improvement on Thurley@?s recent randomized approximation scheme for #k-SAT where the task is to count the number of satisfying truth assignments of a Boolean function @F given as an n-variable k-CNF. We introduce a novel way to identify independent substructures of @F and can therefore reduce the size of the search space considerably. Our randomized algorithm works for any k. For #3-SAT, it runs in time O(@e^-^2@?1.51426^n), for #4-SAT, it runs in time O(@e^-^2@?1.60816^n), with error bound @e.