Publications in Scientific Journals:
S. Ordyniak, D. Paulusma, St. Szeider:
"Satisfiability of acyclic and almost acyclic CNF formulas";
Theoretical Computer Science,
481
(2013),
85
- 99.
English abstract:
We show that the Satisfiability (SAT) problem for CNF formulas with β-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 β-acyclic formulas and this superclass with a number of known polynomial formula classes. We then study the parameterized complexity of SAT for "almost" β-acyclic instances, using as parameter the formula's distance from being β-acyclic. As distance we use the size of a smallest strong backdoor set and the β-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.
Keywords:
Acyclic hypergraph, Chordal bipartite graph, Davis-Putnam resolution
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.tcs.2012.12.039
Related Projects:
Project Head Stefan Szeider:
The Parameterized Complexity of Reasoning Problems
Created from the Publication Database of the Vienna University of Technology.