Backdoors into heterogeneous classes of SAT and CSP

Serge Gaspers, Neeldhara Misra, Sebastian Ordyniak, Stefan Szeider, Stanislav Zivný

Abstract: Highlights•Introduction of Heterogeneous Base classes for SAT and CSP.•Introduction of base classes for CSP defined via polymorphisms.•Complete parameterized complexity classification for strong and weak backdoor set detection for SAT and CSP.•The paper is a largely extended version of the paper with the same title, which appeared in the Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI'14). In addition to containing the full proofs and more detailed explanations, the paper has been extended by the following results:•a complete parameterized complexity classification for strong backdoor set detection for SAT of heterogeneous base classes resulting from combinations of the well-known Schaefer classes,•we now handle not only strong but also weak backdoor sets,•the running times of all strong backdoor set detection algorithms for SAT have been improved from double to single exponential (parameter dependence),•a comparision to related work has been added to the introduction,•a complete comparision to partition backdoor sets has been added as an extra section.