On the Parameterized Complexity of Exact Satisfiability Problems

  • Joachim Kneis
  • Daniel Mölle
  • Stefan Richter
  • Peter Rossmanith
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Joachim Kneis
    • 1
  • Daniel Mölle
    • 1
  • Stefan Richter
    • 1
  • Peter Rossmanith
    • 1
  1. 1.Dept. of Computer ScienceRWTH Aachen UniversityGermany

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