Regular Article
New Upper Bounds for Maximum Satisfiability

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Abstract

The (unweighted) Maximum Satisfiability problem (MaxSat) is: Given a Boolean formula in conjunctive normal form, find a truth assignment that satisfies the largest number of clauses. This paper describes exact algorithms that provide new upper bounds for MaxSat. We prove that MaxSat can be solved in time O(|F| · 1.3803K), where |F| is the length of a formula F in conjunctive normal form and K is the number of clauses in F. We also prove the time bounds O(|F| · 1.3995k), where k is the maximum number of satisfiable clauses, and O(1.1279|F|), for the same problem. For Max2Sat this implies a bound of O(1.2722K).

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  • Cited by (0)

    An extended abstract of this paper was presented at the 26th International Colloquium on Automata, Languages, and Programming (ICALP'99), Prague, Czech Republic, July 11–15, 1999, Lecture Notes in Computer Science, Vol. 1644, pp. 575–584, Springer-Verlag, Berlin/New York.

    f1

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    Supported by a Feodor Lynen fellowship (1998) of the Alexander von Humboldt-Stiftung, Bonn, and the Center for Discrete Mathematics, Theoretical Computer Science and Applications (DIMATIA), Prague.

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