指数困难问题有时是多项式的：随机满意性问题求解算法的大偏差分析及其用于停止-重启求解的应用
无序系统与神经网络
2009-11-07 v1
摘要
presented for random 3-Satisfiability instances slightly below threshold. 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.
引用
@article{arxiv.cond-mat/0203012,
title = {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},
author = {S. Cocco and R. Monasson},
journal= {arXiv preprint arXiv:cond-mat/0203012},
year = {2009}
}
备注
Revtex file, 4 figures