Analysis of a parallel MCMC algorithm for graph coloring with nearly uniform balancing

作     者：Conte, Donatello Grossi, Giuliano Lanzarotti, Raffaella Lin, Jianyi Petrini, Alessandro 

作者机构：Univ Tours Lab Informat Fondamentale & Appl Tours LIFAT EA 6 64 Ave Jean Portalis F-37000 Tours France Univ Milan Dipartimento Informat Via Celoria 18 I-20133 Milan Italy Univ Cattolica Sacro Cuore Dipartimento Sci Stat Largo A Gemelli 1 I-20123 Milan Italy 

出 版 物：《PATTERN RECOGNITION LETTERS》 (模式识别快报)

年 卷 期：2021年第149卷

页      面：30-36页

核心收录：

学科分类：08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：Graph coloring Markov chain Monte Carlo method Color balancing Parallel algorithms 

摘      要：We propose the analysis of a scalable parallel MCMC algorithm for graph coloring aimed at balancing the color class sizes, provided that a suitable number of colors is made available. Firstly, it is shown that the Markov chain converges to the target distribution by repeatedly sampling from suitable proposed distributions over the neighboring colors of each node, independently and hence in parallel manner. We prove that the number of conflicts in the improper colorings genereted thoughout the iterations of the algorithm rapidly converges in probability to 0. As for the balancing, given to the complexity of the distributions involved, we propose a qualitative analysis about the balancing level achieved. Based on a collection of multinoulli distributions arising from the color occurrences within every node neighborhood, we provide some evidence about the character of the final color balancing, which results to be nearly uniform over the color classes. Some numerical simulations on big social graphs confirm the fast convergence and the balancing trend, which is validated through a statistical hypothesis test eventually. (c) 2021 Elsevier B.V. All rights reserved.