Greedy Algorithms for the Minimum Sum Coloring Problem

Greedy algorithms play an important role in the practical resolution of NP-hard problems. A greedy algorithm is a basic heuristic that builds a solution by iteratively adding the locally best element into the solution according to certain criteria. A greedy algorithm can either be used on its own to obtain a “good” solution, or it can be integrated into global optimization methods, for example, to limit the search space in branch and bound algorithms, or to generate initial solutions in metaheuristics. In this paper we are interested in greedy algorithms for the Minimum Sum Coloring Problem (MSCP). Since MSCP is closely related to the basic Graph Coloring Problem (GCP), we start our study with GCP and then turn to MSCP. Concerning GCP, although a lot of work has been reported in the literature, little of it concerns greedy algorithms. The most widely used greedy algorithms remain DSATUR and