A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search

Authors:
Evgeny Dantsin;Andreas Goerdt;Edward A. Hirsch;Ravi Kannan;Jon Kleinberg;Christos Papadimitriou;Prabhakar Raghavan;Uwe Schöning
Affiliations:
Department of Computer Science, University of Manchester, Oxford Road, M13 9PL, UK;TU Chemnitz, Fakultät für Informatik, 09107 Chemnitz, Germany;Steklov Institute of Mathematics, 27 Fontanka, 191011 St. Petersburg, Russia;Department of Computer Science, Yale University, New Haven CT;Department of Computer Science, Cornell University, Ithaca NY;Computer Science Division, Soda Hall, UC Berkeley, CA;Verity Inc., 892 Ross Drive, Sunnyvale CA;Universität Ulm, Abteilung Theoretische Informatik, 89069 Ulm, Germany
Venue:
Theoretical Computer Science
Year:
2002

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Abstract

Local search is widely used for solving the propositional satisfiability problem. Papadimitriou (1991) showed that randomized local search solves 2-SAT in polynomial time. Recently, Schöning (1999) proved that a close algorithm for k-SAT takes time (2 - 2/k)n up to a polynomial factor. This is the best known worst-case upper bound for randomized 3-SAT algorithms (cf. also recent preprint by Schuler et al.).We describe a deterministic local search algorithm for k-SAT running in time (2-2/(k+ 1))n up to a polynomial factor. The key point of our algorithm is the use of covering codes instead of random choice of initial assignments. Compared to other "weakly exponential" algorithms, our algorithm is technically quite simple. We also describe an improved version of local search. For 3-SAT the improved algorithm runs in time 1.481n up to a polynomial factor. Our bounds are better than all previous bounds for deterministic k-SAT algorithms.