Wave Function Collapse Coloring: A New Heuristic for Fast Vertex Coloring

Abstract

In this paper, we propose a high-speed greedy sequential algorithm for the vertex coloring problem (VCP), based on the Wave Function Collapse algorithm, called Wave Function Collapse Coloring (WFC-C). An iteration of this algorithm goes through three distinct phases: vertex selection, color restriction through wave function collapsing, and domain propagation. In effect, WFC-C propagates color choices or "domain" restrictions beyond immediate neighbourhoods. This heuristic, combined with a series of other greedy optimizations, allows for a fast algorithm that prevents certain color conflicts. Through extensive experiments, we show that WFC-C remains competitive (and occasionally better) in terms of optimal coloring, and dramatically outperforms existing high-speed VCP, with on average speed differences ranging from 2000 times to 16000 times, on the most difficult instances of the DIMACS benchmark.