Ann Oper Res
S.I.: CODIT2017-COMBINATORIAL OPTIMIZATION
Minimum spanning tree with conﬂicting edge pairs: a
· Raffaele Cerulli
· 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
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 MSTC solution is a spanning tree without conﬂicts whose total weight is minimal,
i.e., a minimum spanning tree containing at most an edge for each pair in the conﬂict set.
Department of Mathematics, University of Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, SA,