Monte Carlo Graph Coloring

TL;DR

The paper tackles the NP-hard graph coloring problem by modeling it as a Monte Carlo search task and studying two nested algorithms, NMCS and NRPA. It designs problem-specific modeling choices—node ordering with DSatur, forward checking, a monochromatic-edge scoring function, and a compact move encoding—and compares these MC approaches to SAT, HEAD, and Greedy Coloring on standard benchmarks. Results show NRPA generally outperforms NMCS and often rivals HEAD, suggesting that policy adaptation within Monte Carlo search can yield competitive, scalable performance for graph coloring. The work highlights the potential of combining Monte Carlo methods with learning-based policy updates and points to future directions such as graph neural policies and extensions to other coloring variants.

Abstract

Graph Coloring is probably one of the most studied and famous problem in graph algorithms. Exact methods fail to solve instances with more than few hundred vertices, therefore, a large number of heuristics have been proposed. Nested Monte Carlo Search (NMCS) and Nested Rollout Policy Adaptation (NRPA) are Monte Carlo search algorithms for single player games. Surprisingly, few work has been dedicated to evaluating Monte Carlo search algorithms to combinatorial graph problems. In this paper we expose how to efficiently apply Monte Carlo search to Graph Coloring and compare this approach to existing ones.