A branch-and-cut algorithm for the Connected Max-$k$-Cut Problem
Patrick Healya, Nicolas Jozefowiez  1@  , Pierre Laroche, Franc Marchetti, Sébastien Martin, Zsuzsanna Roka@
1 : Laboratoire de Conception, Optimisation et Modélisation des Systèmes  (LCOMS)
Université de Lorraine : EA7306
LCOMS EA7306, Université de Lorraine, Metz 57000, France -  France

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.


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