Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width

Authors Robert Ganian, Petr Hlinený, Jan Obdrzálek

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Robert Ganian
Petr Hlinený
Jan Obdrzálek

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Robert Ganian, Petr Hlinený, and Jan Obdrzálek. Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010). Leibniz International Proceedings in Informatics (LIPIcs), Volume 8, pp. 73-83, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


We provide a parameterized polynomial algorithm for the propositional model counting problem #SAT, the runtime of which is single-exponential in the rank-width of a formula. Previously, analogous algorithms have been known --e.g. [Fischer, Makowsky, and Ravve]-- with a single-exponential dependency on the clique-width of a formula. Our algorithm thus presents an exponential runtime improvement (since clique-width reaches up to exponentially higher values than rank-width), and can be of practical interest for small values of rank-width. We also provide an algorithm for the MAX-SAT problem along the same lines.
  • propositional model counting; satisfiability; rank-width; clique-width ; parameterized complexity


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