Abstract
The performances of a local search procedure, the Pure Random Walk (PRW), for the satisfiability (SAT) problem is investigated with statistical physics methods. We identify and characterize a dynamical transition for the behavior of PRW algorithm on randomly drawn SAT instances where, as the ratio of clauses to variables is increased, the scaling of the solving time changes from being linear to exponential in the input size. A framework for calculating relevant quantities in the linear phase, in particular the average solving time, is introduced, along with an approximate study of the exponential phase.
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Semerjian, G., Monasson, R. (2004). A Study of Pure Random Walk on Random Satisfiability Problems with “Physical” Methods. In: Giunchiglia, E., Tacchella, A. (eds) Theory and Applications of Satisfiability Testing. SAT 2003. Lecture Notes in Computer Science, vol 2919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24605-3_10
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DOI: https://doi.org/10.1007/978-3-540-24605-3_10
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