Skip to Main content Skip to Navigation
New interface
Journal articles

Computational comparisons of different formulations for the Bilevel Minimum Spanning Tree Problem

Martine Labbé 1 Miguel Pozo 2 Justo Puerto 2 
1 INOCS - Integrated Optimization with Complex Structure
Inria Lille - Nord Europe, ULB - Université libre de Bruxelles, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : Let be given a graph G = (V, E) whose edge set is partitioned into a set R of red edges and a set B of blue edges, and assume that red edges are weighted and contain a spanning tree of G. Then, the Bilevel Minimum Spanning Tree Problem (BMSTP) is that of pricing (i.e., weighting) the blue edges in such a way that the total weight of the blue edges selected in a minimum spanning tree of the resulting graph is maximized. In this paper we present different mathematical formulations for the BMSTP based on the properties of the Minimum Spanning Tree Problem and the bilevel optimization. We establish a theoretical and empirical comparison between these new formulations and we also provide reinforcements that together with a proper formulation are able to solve medium to big size instances random instances. We also test our models in instances already existing in the literature.
Document type :
Journal articles
Complete list of metadata
Contributor : Martine Labbé Connect in order to contact the contributor
Submitted on : Tuesday, November 27, 2018 - 7:22:27 PM
Last modification on : Tuesday, November 22, 2022 - 2:26:16 PM


Files produced by the author(s)




Martine Labbé, Miguel Pozo, Justo Puerto. Computational comparisons of different formulations for the Bilevel Minimum Spanning Tree Problem. International Transactions in Operational Research, 2021, ⟨10.1111/itor.12680⟩. ⟨hal-01937013⟩



Record views


Files downloads