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

Author

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  • Francisco J. Aragón Artacho

    (University of Alicante)

  • Rubén Campoy

    (University of Alicante)

  • Veit Elser

    (Cornell University)

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.

Suggested Citation

  • Francisco J. Aragón Artacho & Rubén Campoy & Veit Elser, 2020. "An enhanced formulation for solving graph coloring problems with the Douglas–Rachford algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 383-403, June.
    • Handle: RePEc:spr:jglopt:v:77:y:2020:i:2:d:10.1007_s10898-019-00867-x
    DOI: 10.1007/s10898-019-00867-x
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    References listed on IDEAS

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    1. Joël Benoist, 2015. "The Douglas–Rachford algorithm for the case of the sphere and the line," Journal of Global Optimization, Springer, vol. 63(2), pages 363-380, October.
    2. Francisco J. Aragón Artacho & Jonathan M. Borwein & Matthew K. Tam, 2016. "Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem," Journal of Global Optimization, Springer, vol. 65(2), pages 309-327, June.
    3. A. F. Izmailov & M. V. Solodov & E. I. Uskov, 2016. "Globalizing Stabilized Sequential Quadratic Programming Method by Smooth Primal-Dual Exact Penalty Function," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 148-178, April.
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    Cited by:

    1. Qiao-Li Dong & Songnian He & Michael Th. Rassias, 2021. "General splitting methods with linearization for the split feasibility problem," Journal of Global Optimization, Springer, vol. 79(4), pages 813-836, April.

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