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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CITATION STYLE
de Sousa, E. G., de Andrade, R. C., & Santos, A. C. (2018). A multigraph formulation for the generalized minimum spanning tree problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10856 LNCS, pp. 133–143). Springer Verlag. https://doi.org/10.1007/978-3-319-96151-4_12
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