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We present the Douglas-Rachford algorithm as a successful heuristic forsolving graph coloring problems. Given a set of colors, these type of problemsconsist in assigning a color to each node of a graph, in such a way that everypair of adjacent nodes are assigned with different colors. We formulate thegraph coloring problem as an appropriate feasibility problem that can beeffectively solved by the Douglas-Rachford algorithm, despite the nonconvexityarising from the combinatorial nature of the problem. Different modificationsof the graph coloring problem and applications are also presented. The goodperformance of the method is shown in various computational experiments.

Solving graph coloring problems with the Douglas-Rachford algorithm