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The propositional model counting problem (#SAT) is known to be fixed-parameter-tractable (FPT) when parameterized by the width k of a given tree decomposition of the incidence graph. The running time of the fastest known FPT algorithm contains the exponential factor of. We improve this factor to by utilizing fast algorithms for computing the zeta transform and covering product of functions representing partial model counts, thereby achieving the same running time as FPT algorithms that are parameterized by the less general treewidth of the primal graph. Our new algorithm is asymptotically optimal unless the Strong Exponential Time Hypothesis (SETH) fails.
Slivovsky, F., & Szeider, S. (2020). A Faster Algorithm for Propositional Model Counting Parameterized by Incidence Treewidth. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 12178 LNCS, pp. 267–276). Springer. https://doi.org/10.1007/978-3-030-51825-7_19