🤖 AI Summary
This work addresses the NP-hard large-scale graph coloring problem by systematically adapting Monte Carlo search (MCS) paradigms—specifically Nested Monte Carlo Search (NMCS) and Nested Rollout Policy Adaptation (NRPA)—to this classical combinatorial optimization task for the first time. We propose a graph-coloring-specific state representation, a structured action space modeling, and a conflict-aware heuristic rollout policy, integrated with greedy initialization, dynamic vertex ordering, and conflict-driven backtracking. Experimental evaluation on standard benchmark graphs demonstrates that our approach improves coloring quality by 12–23% over mainstream heuristics—including DSATUR, RLF, and TABUCOL—on instances with over 100 vertices. Moreover, it achieves superior computational efficiency compared to most metaheuristics and significantly surpasses the scalability limits of traditional exact algorithms.
📝 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.