A column generation based algorithm for the robust graph coloring problem

• Published in: Discrete Applied Mathematics Vol. 217; pp. 340 - 352
• Main Authors: Yüceoğlu, Birol, Şahin, Güvenç, van Hoesel, Stan P.M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 30.01.2017; Elsevier BV
• Subjects: Applied mathematics; Coloring; Column generation; Formulations; Graph coloring; Graphs; Reduced cost fixing; Representatives formulation; Robust graph coloring; Scheduling; Set-covering formulation; Robust graph coloring; Column generation; Representatives formulation; Set-covering formulation; Reduced cost fixing
• ISSN: 0166-218X; 1872-6771; 1872-6771
• DOI: 10.1016/j.dam.2016.09.006

Given an undirected simple graph G, an integer k, and a cost cij 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.