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Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
Published on: January 31, 2014
Exponentially hard problems are sometimes polynomial, a large deviation analysis of search algorithms for the random
1CNRS-Laboratoire de Dynamique des Fluides Complexes, 3 rue de l'Université, 67000 Strasbourg, France.
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 is 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 cutoff (the size of the instance) for the restart.
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