Towards a characterisation of the behaviour of stochastic local search algorithms for SAT

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Towards a characterisation of the behaviour of stochastic local search algorithms for SAT (1999)

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by Holger H. Hoos , Thomas Stützle

Venue:	ARTIFICIAL INTELLIGENCE
Citations:	55 - 16 self

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@ARTICLE{Hoos99towardsa,
    author = {Holger H. Hoos and Thomas Stützle},
    title = {Towards a characterisation of the behaviour of stochastic local search algorithms for SAT},
    journal = {ARTIFICIAL INTELLIGENCE},
    year = {1999},
    volume = {112},
    pages = {213--232}
}

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Abstract

Stochastic local search (SLS) algorithms have been successfully applied to hard combinatorial problems from different domains. Due to their inherent randomness, the run-time behaviour of these algorithms is characterised by a random variable. The detailed knowledge of the run-time distribution provides important information about the behaviour of SLS algorithms. In this paper we investigate the empirical run-time distributions for Walksat, one of the most powerful SLS algorithms for the Propositional Satisfiability Problem (SAT). Using statistical analysis techniques, we show that on hard Random-3-SAT problems, Walksat's run-time behaviour can be characterised by exponential distributions. This characterisation can be generalised to various SLS algorithms for SAT and to encoded problems from other domains. This result also has a number of consequences which are of theoretical as well as practical interest. One of these is the fact that these algorithms can be easily parallelised such that optimal speed-up is achieved for hard problem instances.

Keyphrases

stochastic local search algorithm run-time behaviour optimal speed-up detailed knowledge powerful sl algorithm inherent randomness run-time distribution empirical run-time distribution different domain practical interest statistical analysis technique hard problem instance hard random-3-sat problem hard combinatorial problem important information random variable stochastic local search sl algorithm exponential distribution propositional satisfiability problem various sl algorithm

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