Hypergraph Acyclicity and Propositional Model Counting
This provides a new polynomial-time algorithm for a specific class of #SAT instances, which is incremental as it extends known tractable cases but does not solve the general problem.
The paper tackles the #SAT problem for CNF formulas with hypergraphs that have a disjoint branches decomposition, showing it can be solved in polynomial time, and demonstrates that this class is incomparable to previously known tractable classes like bounded incidence cliquewidth.
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.