Abstract
We show that the propositional model counting problem #SAT for CNF-formulas with hypergraphs that allow a disjoint branches decomposition can be solved in polynomial time. We show that this class of hypergraphs is incomparable to hypergraphs of bounded incidence cliquewidth which were the biggest class of hypergraphs for which #SAT was known to be solvable in polynomial time so far. Furthermore, we present a polynomial time algorithm that computes a disjoint branches decomposition of a given hypergraph if it exists and rejects otherwise. Finally, we show that some slight extensions of the class of hypergraphs with disjoint branches decompositions lead to intractable #SAT, leaving open how to generalize the counting result of this paper.
Partially supported by DFG grants BU 1371/2-2 and BU 1371/3-1.
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Capelli, F., Durand, A., Mengel, S. (2014). Hypergraph Acyclicity and Propositional Model Counting. In: Sinz, C., Egly, U. (eds) Theory and Applications of Satisfiability Testing – SAT 2014. SAT 2014. Lecture Notes in Computer Science, vol 8561. Springer, Cham. https://doi.org/10.1007/978-3-319-09284-3_29
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