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.
@InProceedings{ganian_et_al:LIPIcs.FSTTCS.2010.73, author = {Ganian, Robert and Hlinen\'{y}, Petr and Obdrz\'{a}lek, Jan}, title = {{Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2010)}, pages = {73--83}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-23-1}, ISSN = {1868-8969}, year = {2010}, volume = {8}, editor = {Lodaya, Kamal and Mahajan, Meena}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2010.73}, URN = {urn:nbn:de:0030-drops-28541}, doi = {10.4230/LIPIcs.FSTTCS.2010.73}, annote = {Keywords: propositional model counting; satisfiability; rank-width; clique-width ; parameterized complexity} }
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