A satisfiability tester for non-clausal propositional calculus
Information and Computation
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
Vertex cover: further observations and further improvements
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
New Worst-Case Upper Bounds for SAT
Journal of Automated Reasoning
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An algorithm for the SAT problem for formulae of linear length
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Faster exact solving of SAT formulae with a low number of occurrences per variable
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Algorithmics in exponential time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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We present an improved algorithm for the general satisfiability problem. We introduce a new measure, the l -value, for a Boolean formula $\cal F$, which is defined based on weighted variable frequencies in the formula $\cal F$. We then develop a branch-and-search algorithm for the satisfiability problem that tries to maximize the decreasing rates in terms of the l -value during the branch-and-search process. The complexity of the algorithm in terms of the l -value is finally converted into the complexity in terms of the total length L of the input formula, resulting in an algorithm of running time O (20.0911L ) = O (1.0652 L ) for the satisfiability problem, improving the previous best upper bound O (20.0926L ) = O (1.0663 L ) for the problem.