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Mixed-Integer Programming Techniques for the Connected Max-k-Cut Problem

  • We consider an extended version of the classical Max-k-Cut problem in which we additionally require that the parts of the graph partition are connected. For this problem we study two alternative mixed-integer linear formulations and review existing as well as develop new branch-and-cut techniques like cuts, branching rules, propagation, primal heuristics, and symmetry breaking. The main focus of this paper is an extensive numerical study in which we analyze the impact of the different techniques for various test sets. It turns out that the techniques from the existing literature are not sufficient to solve an adequate fraction of the test sets. However, our novel techniques significantly outperform the existing ones both in terms of running times and the overall number of instances that can be solved.

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Author:Christopher Hojny, Imke Joormann, Hendrik Lüthen, Martin SchmidtORCiD
Parent Title (German):Mathematical Programming Computation
Document Type:Article
Language:English
Date of Publication (online):2018/07/26
Release Date:2018/07/26
Tag:Branch-and-cut; Connectivity; Max-cut; Mixed-integer programming
Page Number:45
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Technische Universität Darmstadt
Subprojects:A05
B08
Licence (German):License LogoCreative Commons - CC BY-SA - Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International