Abstract
We propose a simple modification of a well-known Random Walk algorithm for solving the Satisfiability problem and analyze its performance on random CNFs with a planted solution. We rigorously prove that the new algorithm solves the Full CNF with high probability, and for random CNFs with a planted solution of high density finds an assignment that differs from the planted in only ε-fraction of variables. In the experiments the algorithm solves random CNFs with a planted solution of any density.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Achlioptas, D., Sorkin, G.B.: Optimal myopic algorithms for random 3-SAT. In: IEEE Symposium on Foundations of Computer Science, pp. 590–600 (2000)
Alekhnovich, M., Ben-Sasson, E.: Analysis of the random walk algorithm on random 3-CNFs Technical Report ECCC TR04-016 (2002)
Bulatov, A.A., Skvortsov, E.S.: Efficiency of local search. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 297–310. Springer, Heidelberg (2006)
Flaxman, A.: A spectral technique for random satisfiable 3-cnf formulas. In: SODA 2003, pp. 357–363 (2003)
Koutsoupias, E., Papadimitriou, C.: On the greedy algorithm for satisfiability. Information Processing Letters 43(1), 53–55 (1992)
Raghavan, P., Motwani, R.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)
Papadimitriou, C.H.: On selecting a satisfying truth assignment. In: Proceedings of the 32nd Annual IEEE FOCS 1991, pp. 163–169 (1991)
Feige, U., Vilenchik, D.: A local search algorithm for 3sat. Technical report, The Weizmann Institute of Science (2004)
Wormald, N.: Differential equations for random processes and random graphs. The Annals of Applied Probability 5(4), 1217–1235 (1995)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Amiri, E., Skvortsov, E. (2007). Pushing Random Walk Beyond Golden Ratio. In: Diekert, V., Volkov, M.V., Voronkov, A. (eds) Computer Science – Theory and Applications. CSR 2007. Lecture Notes in Computer Science, vol 4649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74510-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-74510-5_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74509-9
Online ISBN: 978-3-540-74510-5
eBook Packages: Computer ScienceComputer Science (R0)