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

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

European Journal of Operational Research, 2024, vol. 312, issue 1, 117-124

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.

Keywords: Combinatorial optimization; Max-cut; Connectivity; Branch-and-cut; Integer programming (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:312:y:2024:i:1:p:117-124

DOI: 10.1016/j.ejor.2023.06.015

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