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

Donatello Conte, Giuliano Grossi, Raffaella Lanzarotti, Jianyi Lin, Alessandro Petrini

Abstract: Highlights•We propose the convergence analysis of a parallel MCMC algorithm for graph coloring.•We prove that, throughout the iterations of the algorithm, the number of color conflicts converges in probability to 0.•We propose a qualitative analysis of the balancing level of the color class sizes achieved.•The parallel algorithm scales well with the graph size.•The effectiveness of the algorithm is assessed on large real-world graphs taken from social analysis.