A branch-and-cut algorithm for the connected max-k-cut problem

Patrick Healy, Nicolas Jozefowiez, Pierre Laroche, Franc Marchetti, Sébastien Martin, Zsuzsanna Róka

Research output: Contribution to journalArticlepeer-review

Abstract

The Connected Max-k-Cut Problem is an extension of the well-known Max-Cut Problem. The objective is to partition a graph into k connected subgraphs by maximizing the cost of inter-partition edges. We propose a new integer linear program for the problem and a branch-and-cut algorithm. We also explore graph isomorphism to structure the instances and facilitate their resolution. We conduct extensive computational experiments on both randomly generated instances and instances from the literature where we compare the quality of our method against existing algorithms. The experimental results show that, if k>2, our approach strictly outperforms those from the literature.

Original languageEnglish
Pages (from-to)117-124
Number of pages8
JournalEuropean Journal of Operational Research
Volume312
Issue number1
DOIs
Publication statusPublished - 1 Jan 2024

Keywords

  • Branch-and-cut
  • Combinatorial optimization
  • Connectivity
  • Integer programming
  • Max-cut

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