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19 April 2024

» arxiv » cond-mat/0203012

Article overview

Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random Satisfiability problem, and its application to stop-and-restart resolutions
S. Cocco ; R. Monasson ;
Date:	1 Mar 2002
Subject:	Disordered Systems and Neural Networks \| cond-mat.dis-nn
Abstract:	A large deviation analysis of the solving complexity of random 3-Satisfiability instances slightly below threshold is presented. While finding a solution for such instances demands an exponential effort with high probability, we show that an exponentially small fraction of resolutions require a computation scaling linearly in the size of the instance only. This exponentially small probability of easy resolutions is analytically calculated, and the corresponding exponent shown to be smaller (in absolute value) than the growth exponent of the typical resolution time. Our study therefore gives some theoretical basis to heuristic stop-and-restart solving procedures, and suggests a natural cut-off (the size of the instance) for the restart.
Source:	arXiv, cond-mat/0203012
Other source:	[GID 69647] pmid12366297
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