New Worst-Case Upper Bounds for SAT
Journal of Automated Reasoning
Faster exact solutions for some NP-hard problems
Theoretical Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Algorithms for four variants of the exact satisfiability problem
Theoretical Computer Science
Exact 3-Satisfiability Is Decidable in Time O(20.16254n)
Annals of Mathematics and Artificial Intelligence
New algorithms for exact satisfiability
Theoretical Computer Science
An algorithm for Exact Satisfiability analysed with the number of clauses as parameter
Information Processing Letters
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The rigorous theoretical analyses of algorithms for exact 3-satisfiability (X3SAT) have been proposed in the literature. As we know, previous algorithms for solving X3SAT have been analyzed only regarding the number of variables as the parameter. However, the time complexity for solving X3SAT instances depends not only on the number of variables, but also on the number of clauses. Therefore, it is significant to exploit the time complexity from the other point of view, i.e. the number of clauses. In this paper, we present algorithms for solving X3SAT with rigorous complexity analyses using the number of clauses as the parameter. By analyzing the algorithms, we obtain the new worst-case upper bounds O (1.15855m ), where m is the number of clauses.