On Solving Exactly and Approximately the Sum Coloring of Graphs

Abstract

In this paper, we tackle the sum coloring problem which is a variant of the graph coloring problem known to be NP-hard. It is an interesting theoretical problem since it can model many applications in scheduling. Sum coloring problem consists on minimizing the sum of colors used to color a graph where colors are represented by naturel numbers (1, 2,. . ., k). In this paper, we present two new mathematical formulation for the underlying problem. We also propose to compute upper bounds using an adaptive iterated multistart tabu search. Experimental results show that the two mathematical formulations were able to solve exactly the NP-hard sum coloring problem. We also report for the first time exact solutions for some tested instances. The proposed tabu search proves its efficiency compared to a basic TABUCOL approach