New Width Parameters for Model Counting

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10491)

Abstract

We study the parameterized complexity of the propositional model counting problem #SAT for CNF formulas. As the parameter we consider the treewidth of the following two graphs associated with CNF formulas: the consensus graph and the conflict graph. Both graphs have as vertices the clauses of the formula; in the consensus graph two clauses are adjacent if they do not contain a complementary pair of literals, while in the conflict graph two clauses are adjacent if they do contain a complementary pair of literals. We show that #SAT is fixed-parameter tractable for the treewidth of the consensus graph but W[1]-hard for the treewidth of the conflict graph. We also compare the new parameters with known parameters under which #SAT is fixed-parameter tractable.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Algorithms and Complexity GroupTU WienViennaAustria

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