FWLS: A Local Search for Graph Coloring

Abstract

Local search (LS) is a widely used, general approach for solving hard combinatorial search problems, such as the graph coloring problem (GCP). One main advantage of this method is that effective heuristics for a problem may lead to improvements in solving other problems. Recently, it has been shown that an initial LS algorithm for the Boolean satisfiability problem (SAT) called WalkSAT is extremely effective for random SAT instances. Thus, it is interesting to apply the heuristics in WalkSAT to GCP. This paper proposes a random walk based heuristic, which is inspired by WalkSAT but differs in the tie-breaking mechanism. This new heuristic leads to a new LS algorithm for GCP namely FWLS. The experiments on the DIMACS benchmark show that FWLS finds optimal (or best known) solutions for most instances. Also, when compared to other GCP algorithms, including a greedy one, an LS one and a hybrid one, FWLS exhibits very competitive or better performance.