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Model Counting for CNF Formulas of Bounded Modular Treewidth Paulusma, Daniel Slivovsky, Friedrich Szeider, Stefan Satisfiability Model Counting Parameterized Complexity 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Daniel Paulusma and Friedrich Slivovsky and Stefan Szeider 2013 Is Part Of LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2013.55 urn:nbn:de:0030-drops-39226 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.55 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode