THE GLAUBER DYNAMICS FOR COLORINGS OF BOUNDED DEGREE TREES

被引：8

作者：

Lucier, B. ^{[1
]}

Molloy, M. ^{[1
]}

机构：

[1] Univ Toronto, Dept Comp Sci, Toronto, ON M4E 3G1, Canada

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2011年 / 25卷 / 02期

关键词：

Glauber dynamics; block dynamics; coloring;

D O I：

10.1137/090779516

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Glauber dynamics Markov chain for k-colorings of trees with maximum degree Delta. For k >= 3, we show that the mixing time on the complete tree is n(theta(1+Delta/(k log Delta))). For k >= 4 we extend our analysis to show that the mixing time on any tree is at most n(O(1+Delta/(k log Delta))). Our proof uses a weighted canonical paths analysis and introduces a variation of the block dynamics that exploits the differing relaxation times of blocks.

引用

页码：827 / 853

页数：27

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