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@inproceedings{1414044, author = {Ganian, Robert and Ramanujan, M.S. and Szeider, Stefan}, address = {Nemecko}, booktitle = {Theory and Applications of Satisfiability Testing - SAT 2017 - 20th International Conference, Melbourne, VIC, Australia, August 28 - September 1, 2017, Proceedings}, doi = {http://dx.doi.org/10.1007/978-3-319-66263-3_2}, edition = {10491}, editor = {Serge Gaspers and Toby Walsh}, keywords = {Treewidth; Parameterized Complexity; SAT; Backdoors}, howpublished = {elektronická verze "online"}, language = {eng}, location = {Nemecko}, isbn = {978-3-319-66262-6}, pages = {20-37}, publisher = {Springer}, title = {Backdoor Treewidth for SAT}, url = {https://link.springer.com/chapter/10.1007/978-3-319-66263-3_2}, year = {2017} }
TY - JOUR ID - 1414044 AU - Ganian, Robert - Ramanujan, M.S. - Szeider, Stefan PY - 2017 TI - Backdoor Treewidth for SAT PB - Springer CY - Nemecko SN - 9783319662626 KW - Treewidth KW - Parameterized Complexity KW - SAT KW - Backdoors UR - https://link.springer.com/chapter/10.1007/978-3-319-66263-3_2 L2 - https://link.springer.com/chapter/10.1007/978-3-319-66263-3_2 N2 - A strong backdoor in a CNF formula is a set of variables such that each possible instantiation of these variables moves the formula into a tractable class. The algorithmic problem of finding a strong backdoor has been the subject of intensive study, mostly within the parameterized complexity framework. Results to date focused primarily on backdoors of small size. In this paper we propose a new approach for algorithmically exploiting strong backdoors for SAT: instead of focusing on small backdoors, we focus on backdoors with certain structural properties. In particular, we consider backdoors that have a certain tree-like structure, formally captured by the notion of backdoor treewidth. First, we provide a fixed-parameter algorithm for SAT parameterized by the backdoor treewidth w.r.t. the fundamental tractable classes Horn, Anti-Horn, and 2CNF. Second, we consider the more general setting where the backdoor decomposes the instance into components belonging to different tractable classes, albeit focusing on backdoors of treewidth 1 (i.e., acyclic backdoors). We give polynomial-time algorithms for SAT and #SAT for instances that admit such an acyclic backdoor. ER -
GANIAN, Robert, M.S. RAMANUJAN and Stefan SZEIDER. Backdoor Treewidth for SAT. Online. In Serge Gaspers and Toby Walsh. \textit{Theory and Applications of Satisfiability Testing - SAT 2017 - 20th International Conference, Melbourne, VIC, Australia, August 28 - September 1, 2017, Proceedings}. 10491st ed. Nemecko: Springer, 2017, p.~20-37. ISBN~978-3-319-66262-6. Available from: https://dx.doi.org/10.1007/978-3-319-66263-3\_{}2.
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