Abstract
This paper is devoted to a rigorous analysis of the GSAT algorithm in the typical case for the random planted 3-SAT distribution. GSAT was the first widely appreciated practical heuristic developed for SAT that was based on the local search principles. We show that for any constant κ> 0 GSAT, with high probability, solves random planted 3-SAT problems of density ρ = κln n. This performance is substantially better than the performance of the pure Iterative Improvement algorithm that has a phase transition at \(\rho = \frac{7}{6} \ln n\) and fails for problems of smaller density.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bulatov, A.A., Skvortsov, E.S.: Phase transition for local search on planted SAT. CoRR, abs/0811.2546 (2008)
Feige, U., Vilenchik, D.: A local search algorithm for 3SAT. Technical report MCS04-07 of the Weizmann Institute (2004)
Flaxman, A.: A spectral technique for random satisfiable 3CNF formulas. In: SODA, pp. 357–363 (2003)
Gent, I.: On the stupid algorithm for Satisfiability. Ian. Gent. APES Report APES-03-1998. APES Research Group (1998)
Gent, I.P., Bridge, S., Walsh, T.: An empirical analysis of search in GSAT. Journal of Artificial Intelligence Research 1, 47–59 (1993)
Gent, I.P., Walsh, T.: The enigma of SAT hill-climbing procedures. Technical report, Department of AI, University of Edinburgh (1992)
Gent, I.P., Walsh, T.: Towards an understanding of hill-climbing procedures for SAT. In: AAAI, pp. 28–33 (1993)
Hansen, P., Jaumard, B.: Algorithms for the maximum Satisfiability problem. Computing 44, 279–303 (1990)
Hirsch, E.A.: SAT local search algorithms: Worst-case study. J. Autom. Reason 24(1-2), 127–143 (2000)
Hoos, H., Sttzle, T.: Stochastic Local Search: Foundations & Applications. Morgan Kaufmann Publishers Inc., San Francisco (2004)
Koutsoupias, E., Papadimitriou, C.: On the greedy algorithm for Satisfiability. Inf. Process. Lett. 43(1), 53–55 (1992)
Mastrolilli, M., Gambardella, L.M.: Maximum satisfiability: How good are tabu search and plateau moves in the worst-case? European Journal of Operational Research 166(1), 63–76 (2005)
Selman, B., Levesque, H., Mitchell, D.: A new method for solving hard satisfiability problems. In: AAAI, pp. 440–446 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Skvortsov, E.S. (2009). A Theoretical Analysis of Search in GSAT. In: Kullmann, O. (eds) Theory and Applications of Satisfiability Testing - SAT 2009. SAT 2009. Lecture Notes in Computer Science, vol 5584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02777-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-642-02777-2_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02776-5
Online ISBN: 978-3-642-02777-2
eBook Packages: Computer ScienceComputer Science (R0)