We present the current fastest deterministic algorithm for k-SAT, improving the upper bound (2-2/k)^{n + o(n)} due to Moser and Scheder in STOC 2011. The algorithm combines a branching algorithm with the derandomized local search, whose analysis relies on a special sequence of clauses called chain, and a generalization of covering code based on linear programming. We also provide a more intelligent branching algorithm for 3-SAT to establish the upper bound 1.32793^n, improved from 1.3303^n.
@InProceedings{liu:LIPIcs.ICALP.2018.88, author = {Liu, Sixue}, title = {{Chain, Generalization of Covering Code, and Deterministic Algorithm for k-SAT}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {88:1--88:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.88}, URN = {urn:nbn:de:0030-drops-90925}, doi = {10.4230/LIPIcs.ICALP.2018.88}, annote = {Keywords: Satisfiability, derandomization, local search} }
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