Minimum conflict balanced graph coloring problem

Abstract

Graph coloring is an important problem in optimization. The classical vertex coloring problem in graphs asks that the vertices are clustered to groups (colors) having no edge interconnections. In this thesis, we focus on a di erent version of the vertex coloring problem. The vertices have to be partitioned into balanced groups with a minimum number of con icts (inner-group connections). In mobile wireless communications, this version of the problem has several applications. Since the majority of graph coloring problems are NP-hard, only a few exact methods have been introduced in the literature. We propose several mixed-integer linear programming formulations that are solved within a binary search framework and show their e cacy. In order to provide lower and upper bounds to our problem, we use clique inequalities as valid inequalities and a heuristic algorithm, respectively. We perform computational analyses instances from the literature and also on instances that we randomly generate. We compare performances of models/algorithms in terms of their solution times and also conduct sensitivity analyses using di erent parameter settings on randomly generated instances and discuss their e ects on the solution times.