An enhanced formulation for solving graph coloring problems with the Douglas–Rachford algorithm

Francisco J. Aragón Artacho (), Rubén Campoy () and Veit Elser ()
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Francisco J. Aragón Artacho: University of Alicante
Rubén Campoy: University of Alicante
Veit Elser: Cornell University

Journal of Global Optimization, 2020, vol. 77, issue 2, No 9, 383-403

Abstract: Abstract We study the behavior of the Douglas–Rachford algorithm on the graph vertex-coloring problem. Given a graph and a number of colors, the goal is to find a coloring of the vertices so that all adjacent vertex pairs have different colors. In spite of the combinatorial nature of this problem, the Douglas–Rachford algorithm was recently shown to be a successful heuristic for solving a wide variety of graph coloring instances, when the problem was cast as a feasibility problem on binary indicator variables. In this work we consider a different formulation, based on semidefinite programming. The much improved performance of the Douglas–Rachford algorithm, with this new approach, is demonstrated through various numerical experiments.

Keywords: Douglas–Rachford algorithm; Graph coloring; Feasibility problem; Nonconvex constraints; 47J25; 90C27; 47N10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-019-00867-x

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