Abstract
Given a connected, undirected and m-partite complete graph \(G = (V_1 \cup V_2 \cup ... \cup V_m; E)\), the Generalized Minimum Spanning Tree Problem (GMSTP) consists in finding a tree with exactly \(m - 1\) edges, connecting the m clusters \(V_1, V_2, ..., V_m\) 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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Acknowledgements
The authors are grateful to CNPq (grant 449254/2014-3) and FUNCAP (grant PNE-0112-00061.01.00/16) and to the anonymous referees for their helpful comments.
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de Sousa, E.G., de Andrade, R.C., Santos, A.C. (2018). A Multigraph Formulation for the Generalized Minimum Spanning Tree Problem. In: Lee, J., Rinaldi, G., Mahjoub, A. (eds) Combinatorial Optimization. ISCO 2018. Lecture Notes in Computer Science(), vol 10856. Springer, Cham. https://doi.org/10.1007/978-3-319-96151-4_12
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