On the parameterized complexity of exact satisfiability problems

Authors:
Joachim Kneis;Daniel Mölle;Stefan Richter;Peter Rossmanith
Affiliations:
Dept. of Computer Science, RWTH Aachen University, Germany;Dept. of Computer Science, RWTH Aachen University, Germany;Dept. of Computer Science, RWTH Aachen University, Germany;Dept. of Computer Science, RWTH Aachen University, Germany
Venue:
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Year:
2005

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Abstract

For many problems, the investigation of their parameterized complexity provides an interesting and useful point of view. The most obvious natural parameterization for the maximum satisfiability problem—the number of satisfiable clauses—makes little sense, because at least half of the clauses can be satisfied in any formula. We look at two optimization variants of the exact satisfiability problem, where a clause is only said to be fulfilled iff exactly one of its literals is set to true. Interestingly, these variants behave quite differently. In the case of ResMaxExactSAT, where over-satisfied clauses are entirely forbidden, we show fixed parameter tractability. On the other hand, if we choose to ignore over-satisfied clauses, the MaxExactSAT problem is obtained. Surprisingly, it is W[1]-complete. Still, restricted variants of the problem turn out to be tractable.