Perfect sampling from spatial mixing.

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2022-12-01 Epub Date: 2022-02-18 DOI:10.1002/rsa.21079

Weiming Feng, Heng Guo, Yitong Yin

引用次数: 0

Abstract

We introduce a new perfect sampling technique that can be applied to general Gibbs distributions and runs in linear time if the correlation decays faster than the neighborhood growth. In particular, in graphs with subexponential neighborhood growth like $ℤ^{d}$ , our algorithm achieves linear running time as long as Gibbs sampling is rapidly mixing. As concrete applications, we obtain the currently best perfect samplers for colorings and for monomer-dimer models in such graphs.

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完美的空间混合采样

我们引入了一种新的完美采样技术，它可以应用于一般的吉布斯分布，而且如果相关性的衰减速度快于邻域增长速度，运行时间也是线性的。特别是在ℤ d 这样具有亚指数邻域增长的图中，只要吉布斯采样快速混合，我们的算法就能实现线性运行时间。在具体应用中，我们得到了目前在这类图中用于着色和单体-二聚体模型的最佳完美采样器。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.