Solving k-way graph partitioning problems to optimality: The impact of semidefinite relaxations and the bundle method

Anjos M, Ghaddar B, Hupp L, Liers F, Wiegele A (2013)

Publication Status: Published

Publication Type: Book chapter / Article in edited volumes

Publication year: 2013

Publisher: Springer-Verlag Berlin Heidelberg

Edited Volumes: Facets of Combinatorial Optimization

Book Volume: 9783642381898

Pages Range: 355-386

ISBN: 9783642381881

DOI: 10.1007/978-3-642-38189-8_15

Abstract

This paper is concerned with computing global optimal solutions for maximum k-cut problems. We improve on the SBC algorithm of Ghaddar, Anjos and Liers in order to compute such solutions in less time. We extend the design principles of the successful BiqMac solver for maximum 2-cut to the general maximum k-cut problem. As part of this extension, we investigate different ways of choosing variables for branching. We also study the impact of the separation of clique inequalities within this new framework and observe that it frequently reduces the number of subproblems considerably. Our computational results suggest that the proposed approach achieves a drastic speedup in comparison to SBC, especially when k=3. We also made a comparison with the orbitopal fixing approach of Kaibel, Peinhardt and Pfetsch. The results suggest that, while their performance is better for sparse instances and larger values of k, our proposed approach is superior for smaller k and for dense instances of medium size. Furthermore, we used CPLEX for solving the ILP formulation underlying the orbitopal fixing algorithm and conclude that especially on dense instances the new algorithm outperforms CPLEX by far.

Authors with CRIS profile

Lena Hupp
Frauke Liers-Bergmann Professur für Optimization under Uncertainty & Data Analysis

Involved external institutions

University of Waterloo (UW) CA Canada (CA) Alpen-Adria-Universität Klagenfurt AT Austria (AT)

How to cite

APA:

Anjos, M., Ghaddar, B., Hupp, L., Liers, F., & Wiegele, A. (2013). Solving k-way graph partitioning problems to optimality: The impact of semidefinite relaxations and the bundle method. In Michael Jünger, Gerhard Reinelt (Eds.), Facets of Combinatorial Optimization. (pp. 355-386). Springer-Verlag Berlin Heidelberg.

MLA:

Anjos, Miguel, et al. "Solving k-way graph partitioning problems to optimality: The impact of semidefinite relaxations and the bundle method." Facets of Combinatorial Optimization. Ed. Michael Jünger, Gerhard Reinelt, Springer-Verlag Berlin Heidelberg, 2013. 355-386.

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