Using Graph Isomorphism Network to Solve Graph Coloring Problem

The graph coloring problem is a classical NP-hard combinatorial optimization problem, which aims to assign distinct colors to connected nodes as much as possible. Currently, graph neural networks are being applied to combinatorial optimization problems but have not yielded satisfactory experimental results. This paper discusses the advantages and challenges of different types of graph neural networks in solving the graph coloring problem. It is deduced that graph isomorphism networks possess stronger coloring abilities than other types of graph neural networks in theory, leading to a graph isomorphism network model based on physical-inspired framework and tabu search algorithm to solve the graph coloring problem. The theoretical findings have been empirically validated, demonstrating that the proposed model performs comparably or superiorly to existing solvers in terms of both quality and running time.