Abstract
This paper presents a detailed empirical study of local search for Boolean satisfiability (SAT), highlighting several interesting properties, some of which were previously unknown or had only anecdotal evidence. Specifically, we study hard random 3-CNF formulas and provide surprisingly simple analytical fits for the optimal (static) noise level and the runtime at optimal noise, as a function of the clause-to-variable ratio. We also demonstrate, for the first time for local search, a power-law decay in the tail of the runtime distribution in the low noise regime. Finally, we discuss a Markov Chain model capturing this intriguing feature.
Supported by NSF (Expeditions in Computing award for Computational Sustainability, 0832782; IIS grant 0514429) & AFOSR (IISI, grant FA9550-04-1-0151). The authors thank Yahoo! for generously providing access to their M45 compute cloud.
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Kroc, L., Sabharwal, A., Selman, B. (2010). An Empirical Study of Optimal Noise and Runtime Distributions in Local Search. In: Strichman, O., Szeider, S. (eds) Theory and Applications of Satisfiability Testing – SAT 2010. SAT 2010. Lecture Notes in Computer Science, vol 6175. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14186-7_31
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DOI: https://doi.org/10.1007/978-3-642-14186-7_31
Publisher Name: Springer, Berlin, Heidelberg
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