Satisfiability of acyclic and almost acyclic CNF formulas
| Authors | |
|---|---|
| Year of publication | 2013 |
| Type | Article in Periodical |
| Magazine / Source | Theoretical Computer Science |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1016/j.tcs.2012.12.039 |
| Field | Information theory |
| Keywords | Acyclic hypergraph; Chordal bipartite graph; Davis-Putnam resolution |
| Description | We show that the SATISFIABILITY (SAT) problem for CNF formulas with beta-acyclic hypergraphs can be solved in polynomial time by using a special type of Davis-Putnam resolution in which each resolvent is a subset of a parent clause. We extend this class to CNF formulas for which this type of Davis-Putnam resolution still applies and show that testing membership in this class is NP-complete. We compare the class of beta-acyclic formulas and this superclass with a number of known polynomial formula classes. We then study the parameterized complexity of SAT for "almost" beta-acyclic instances, using as parameter the formula's distance from being beta-acyclic. As distance we use the size of a smallest strong backdoor set and the beta-hypertree width. As a by-product we obtain the W[1]-hardness of SAT parameterized by the (undirected) clique-width of the incidence graph, which disproves a conjecture by Fischer, Makowsky, and Ravve. (C) 2013 Elsevier B.V. All rights reserved. |
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