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A Multigraph Formulation for the Generalized Minimum Spanning Tree Problem

Abstract

Given a connected, undirected and m-partite complete graph G=(V1∪V2∪...∪Vm;E), the Generalized Minimum Spanning Tree Problem (GMSTP) consists in finding a tree with exactly m−1 edges, connecting the m clusters V1,V2,...,Vm through the selection of a unique vertex in each cluster. GMSTP finds applications in network design, irrigation agriculture, smart cities, data science, among others. This paper presents a new multigraph mathematical formulation for GMSTP which is compared to existing formulations from the literature. The proposed model proves optimality for well-known GMSTP instances. In addition, this work opens new directions for future research to the development of sophisticated cutting plane and decomposition algorithms for related problems.
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Dates and versions

hal-02291657 , version 1 (19-09-2019)

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Ernando Gomes de Sousa, Rafael Castro de Andrade, Andréa Cynthia Santos. A Multigraph Formulation for the Generalized Minimum Spanning Tree Problem. ISCO 2018: Combinatorial Optimization, 10856, Springer, pp.133-143, 2018, Lecture Notes in Computer Science, ⟨10.1007/978-3-319-96151-4_12⟩. ⟨hal-02291657⟩

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