Model counting for CNF formuals of bounded module treewidth

Paulusma, D.; Slivovksy, F.; Szeider, S.

Abstract

The modular treewidth of a graph is its treewidth after the contraction of modules. Modular treewidth properly generalizes treewidth and is itself properly generalized by clique-width. We show that the number of satisfying assignments of a CNF formula whose incidence graph has bounded modular treewidth can be computed in polynomial time. This provides new tractable classes of formulas for which #SAT is polynomial. In particular, our result generalizes known results for the treewidth of incidence graphs and is incomparable with known results for clique-width (or rank-width) of signed incidence graphs. The contraction of modules is an effective data reduction procedure. Our algorithm is the first one to harness this technique for #SAT. The order of the polynomial time bound of our algorithm depends on the modular treewidth. We show that this dependency cannot be avoided subject to an assumption from Parameterized Complexity.

Citation

Paulusma, D., Slivovksy, F., & Szeider, S. (2013, December). Model counting for CNF formuals of bounded module treewidth. Presented at 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013), Kiel, Christian-Albrechts-Universität zu Kiel, Germany

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
• Publication Date: Jan 1, 2013
• Deposit Date: Mar 11, 2013
• Publicly Available Date: Jan 8, 2015
• Pages: 55-66
• Series Title: Leibniz International Proceedings in Informatics (LIPIcs)
• Series Number: 20
• Series ISSN: 1868-8969
• Book Title: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013).
• ISBN: 9783939897507
• DOI: https://doi.org/10.4230/lipics.stacs.2013.55
• Keywords: Satisfiability, Model Counting, Parameterized Complexity.
• Public URL: https://durham-repository.worktribe.com/output/1156230
• Additional Information: Conference dates: Feb 27–Mar 2, 2013