Accelerating simulated annealing for the permanent and combinatorial counting problems

被引：47

作者：

Bezakova, Ivona ^{[1
]}

Stefankovic, Daniel ^{[2
]}

Vazirani, Vijay V. ^{[3
]}

Vigoda, Eric ^{[3
]}

机构：

[1] Rochester Inst Technol, Dept Comp Sci, Rochester, NY 14623 USA

[2] Univ Rochester, Dept Comp Sci, Rochester, NY 14627 USA

[3] Georgia Inst Technol, Coll Comp, Atlanta, GA 30332 USA

来源：

SIAM JOURNAL ON COMPUTING | 2008年 / 37卷 / 05期

关键词：

Markov chain Monte Carlo; simulated annealing; cooling schedule; approximate counting problems;

D O I：

10.1137/050644033

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We present an improved "cooling schedule" for simulated annealing algorithms for combinatorial counting problems. Under our new schedule the rate of cooling accelerates as the temperature decreases. Thus, fewer intermediate temperatures are needed as the simulated annealing algorithm moves from the high temperature (easy region) to the low temperature (difficult region). We present applications of our technique to colorings and the permanent (perfect matchings of bipartite graphs). Moreover, for the permanent, we improve the analysis of the Markov chain underlying the simulated annealing algorithm. This improved analysis, combined with the faster cooling schedule, results in an O(n(7)log(4)n) time algorithm for approximating the permanent of a 0/1 matrix.

引用

页码：1429 / 1454

页数：26

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