A column generation based algorithm for the robust graph coloring problem

Abstract

Given an undirected simple graph $G$, an integer $k$, and a cost $c_{ij}$ for each pair of non-adjacent vertices in $G$, a robust coloring of $G$ is the assignment of $k$ colors to vertices such that adjacent vertices get different colors and the total penalty of the pairs of vertices having the same color is minimum. The problem has applications in fields such as timetabling and scheduling. We present a new formulation for the problem, which extends an existing formulation for the graph coloring problem. We also discuss a column generation based solution method. We report computational study on the performance of alternative formulations and the column generation method.