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 , 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-complete, for certain tractable cases. These are the first completeness results in lower levels of the W-hierarchy for any backdoor set problems.
Journal on Satisfiability, Boolean Modeling and Computation ISSN: 1574-0617
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JSAT volume 12
Volume for papers published in 2020.
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Abstract: This paper is a system description of the anytime MaxSAT solver TT-Open-WBO-Inc, which won both of the weighted incomplete tracks of MaxSAT Evaluation 2019. We implemented the recently introduced polarity and variable selection heuristics, TORC and TSB, respectively, in the Open-WBO-Inc-BMO algorithm within the open-source anytime MaxSAT solver Open-WBO-Inc. As a result, the solver is substantially more efficient.Software