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MADAM: a parallel exact solver for max-cut based on semidefinite programming and ADMM

Author

Listed:
  • Timotej Hrga

    (University of Ljubljana)

  • Janez Povh

    (University of Ljubljana
    Institute of Mathematics, Physics and Mechanics Ljubljana)

Abstract

We present MADAM, a parallel semidefinite-based exact solver for Max-Cut, a problem of finding the cut with the maximum weight in a given graph. The algorithm uses the branch and bound paradigm that applies the alternating direction method of multipliers as the bounding routine to solve the basic semidefinite relaxation strengthened by a subset of hypermetric inequalities. The benefit of the new approach is a less computationally expensive update rule for the dual variable with respect to the inequality constraints. We provide a theoretical convergence of the algorithm as well as extensive computational experiments with this method, to show that our algorithm outperforms state-of-the-art approaches. Furthermore, by combining algorithmic ingredients from the serial algorithm, we develop an efficient distributed parallel solver based on MPI.

Suggested Citation

  • Timotej Hrga & Janez Povh, 2021. "MADAM: a parallel exact solver for max-cut based on semidefinite programming and ADMM," Computational Optimization and Applications, Springer, vol. 80(2), pages 347-375, November.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:2:d:10.1007_s10589-021-00310-6
    DOI: 10.1007/s10589-021-00310-6
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    References listed on IDEAS

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    1. Iain Dunning & Swati Gupta & John Silberholz, 2018. "What Works Best When? A Systematic Evaluation of Heuristics for Max-Cut and QUBO," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 608-624, August.
    2. Fischer, I. & Gruber, G. & Rendl, F. & Sotirov, R., 2006. "Computational experience with a bundle approach for semidenfinite cutting plane relaxations of max-cut and equipartition," Other publications TiSEM 03dfd8c3-9216-4c75-8921-3, Tilburg University, School of Economics and Management.
    3. Laura Palagi & Veronica Piccialli & Franz Rendl & Giovanni Rinaldi & Angelika Wiegele, 2012. "Computational Approaches to Max-Cut," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 821-847, Springer.
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