Journal on Satisfiability, Boolean Modeling and Computation ISSN: 1574-0617

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JSAT volume 12

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Table of Contents

Backdoors into Two Occurrences, Jan Johannsen, 1-15. Backdoor set fixed-parameter tractability parameterized complexity completeness formulas with two variable occurrences
Abstract: Backdoor sets for the class CNF(2) of CNF-formulas in which every variable has at most two occurrences are studied in terms of parameterized complexity. The question whether there exists a CNF(2)-backdoor set of size k is hard for the class W[2] , for both weak and strong backdoors, and in both cases it becomes fixed-parameter tractable when restricted to inputs in d-CNF for a fixed d . Besides that, it is shown that the problem of finding weak backdoor sets is W[2]-complete, for certain tractable cases. These are the first completeness results in lower levels of the W-hierarchy for any backdoor set problems.