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Reference:
Mikko Alava, John Ardelius, Erik Aurell, Petteri Kaski, Supriya Krishnamurthy, and Pekka Orponen. Circumspect descent prevails in solving random constraint satisfaction problems. Proceedings of the National Academy of Sciences (USA), 105(40):15253–15257, October 2008.
Abstract:
We study the performance of stochastic local search algorithms for random instances of the  -satisfiability (-SAT) problem. We introduce a new stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large -SAT instances almost surely in linear time, up to high clause-to-variable ratios  ; for example, for  we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.
Keywords:
local search, random -SAT, performance, geometry of solutions
Suggested BibTeX entry:
@article{AAAK08,
author = {Mikko Alava and John Ardelius and Erik Aurell and Petteri Kaski and Supriya Krishnamurthy and Pekka Orponen},
journal = {Proceedings of the National Academy of Sciences (USA)},
month = {October},
number = {40},
pages = {15253--15257},
title = {Circumspect descent prevails in solving random constraint satisfaction problems},
volume = {105},
year = {2008},
}
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