An empirical study of optimal noise and runtime distributions in local search

Authors:
Lukas Kroc;Ashish Sabharwal;Bart Selman
Affiliations:
Dept. of Computer Science, Cornell University, Ithaca, NY;Dept. of Computer Science, Cornell University, Ithaca, NY;Dept. of Computer Science, Cornell University, Ithaca, NY
Venue:
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
Year:
2010

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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.