An effective heuristic algorithm for sum coloring of graphs

Given an undirected graph $G=(V,E)$ , the minimum sum coloring problem (MSCP) is to find a legal vertex coloring of G, using colors represented by natural numbers $(\mathrm{1,2},\dots )$ such that the total sum of the colors assigned to the vertices is minimized. In this paper, we present EXSCOL, a heuristic algorithm based on independent set extraction for this NP‐hard problem. EXSCOL identifies iteratively collections of disjoint independent sets of equal size and assign to each independent set the smallest available color. For the purpose of computing large independent sets, EXSCOL employs a tabu search based heuristic. Experimental evaluations on a collection of 52 DIMACS and COLOR2 benchmark graphs show that the proposed approach achieves highly competitive results. For more than half of the graphs used in the literature, our approach improves the current best known upper bounds.