Ann Oper Res https://doi.org/10.1007/s10479-018-2895-y S.I.: CODIT2017-COMBINATORIAL OPTIMIZATION Minimum spanning tree with conﬂicting edge pairs: a branch-and-cut approach 1 1 Francesco Carrabs · Raffaele Cerulli · 1 1 Rosa Pentangelo · Andrea Raiconi © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this paper, we show a branch-and-cut approach to solve the minimum spanning tree problem with conﬂicting edge pairs. This is a NP-hard variant of the classical minimum spanning tree problem, in which there are mutually exclusive edges. We introduce a new set of valid inequalities for the problem, based on the properties of its feasible solutions, and we develop a branch-and-cut algorithm based on them. Computational tests are performed both on benchmark instances coming from the literature and on some newly proposed ones. Results show that our approach outperforms a previous branch-and-cut algorithm proposed for the same problem. Keywords Minimum spanning tree · Conﬂicting edges · Branch-and-cut 1 Introduction The minimum spanning tree problem with conﬂicting edge pairs (MSTC) is a very recent variant of the classical minimum spanning tree (MST) problem. Given a connected, undi- rected and edge-weighted graph, as well as a set of edges pairs in conﬂict with each other, a feasible
Annals of Operations Research – Springer Journals
Published: May 29, 2018
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