Faster Exact Solutions for Some NP-Hard Problems
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
New algorithms for exact satisfiability
Theoretical Computer Science
The worst-case upper bound for exact 3-satisfiability with the number of clauses as the parameter
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
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Let F=C1∧⋅⋅⋅∧Cm be a Boolean formula in conjunctive normal form over a set V of n propositional variables, s.t. each clause Ci contains at most three literals l over V. Solving the problem exact 3-satisfiability (X3SAT) for F means to decide whether there is a truth assignment setting exactly one literal in each clause of F to true (1). As is well known X3SAT is NP-complete [6]. By exploiting a perfect matching reduction we prove that X3SAT is deterministically decidable in time O(20.18674n). Thereby we improve a result in [2,3] stating X3SAT∈O(20.2072n) and a bound of O(20.200002n) for the corresponding enumeration problem #X3SAT stated in a preprint [1]. After that by a more involved deterministic case analysis we are able to show that X3SAT∈O(20.16254n).