Algorithms for four variants of the exact satisfiability problem

  • Authors:

  • Vilhelm Dahllöf;Peter Jonsson;Richard Beigel

  • Affiliations:

  • Department of Computer and Information Science, Linköping University, SE-581 83 Linköping, Sweden;Department of Computer and Information Science, Linköping University, SE-581 83 Linköping, Sweden;Department of Computer and Information Sciences, Temple University, 1805 N Broad St Fl 4, Philadelphia, PA

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2004

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Abstract

We present four polynomial space and exponential time algorithms for variants of the EXACT SATISFIABILITY problem. First, an O(1.1120n) (where n is the number of variables) time algorithm for the NP-complete decision problem of EXACT 3-SATISFIABILITY, and then an O(1.1907n) time algorithm for the general decision problem of EXACT SATISFIABILITY. The best previous algorithms run in O(1.1193n) and O(1.2299n) time, respectively. For the #P-complete problem of counting the number of models for EXACT 3-SATISFIABILITY we present an O(1.1487n) time algorithm. We also present an O(1.2190n) time algorithm for the general problem of counting the number of models for EXACT SATISFIABILITY; presenting a simple reduction, we show how this algorithm can be used for computing the permanent of a 0/1 matrix.