New Integer Linear Programming Models for the Vertex Coloring Problem
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The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that each two neighbors have different colors. The problem is NP-hard. Here, we introduce new integer linear programming formulations based on partial-ordering. They have the advantage that they are as simple to work with as the classical assignment formulation, since they can be fed directly into a standard integer linear programming solver. We evaluate our new models using Gurobi and show that our new simple approach is a good alternative to the best state-of-the-art approaches for the vertex coloring problem. In our computational experiments, we compare our formulations with the classical assignment formulation and the representatives formulation on a large set of benchmark graphs as well as randomly generated graphs of varying size and density. The evaluation shows that the partial-ordering based models dominate both formulations for sparse graphs, while the representatives formulation is the best for dense graphs.
KeywordsGraph coloring Vertex coloring Integer linear programming
This work was partially supported by DFG, RTG 1855.
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