Hypergraph Acyclicity and Propositional Model Counting
| Autor: | Arnaud Durand, Florent Capelli, Stefan Mengel |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Model counting
Discrete mathematics Class (set theory) Hypergraph TheoryofComputation_COMPUTATIONBYABSTRACTDEVICES Mathematics::Combinatorics Disjoint sets Combinatorics TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES #SAT Computer Science::Discrete Mathematics TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY Bounded function Time complexity MathematicsofComputing_DISCRETEMATHEMATICS Incidence (geometry) Mathematics |
| Zdroj: | Lecture Notes in Computer Science ISBN: 9783319092836 SAT |
| DOI: | 10.1007/978-3-319-09284-3_29 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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