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. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Kneis, J., Mölle, D., Richter, S., & Rossmanith, P. (2005). On the parameterized complexity of exact satisfiability problems. In Lecture Notes in Computer Science (Vol. 3618, pp. 568–579). Springer Verlag. https://doi.org/10.1007/11549345_49
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