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The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances

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  • Pop, Petrică C.

Abstract

In this paper, some of the main known results relative to the generalized minimum spanning tree problem are surveyed. The principal feature of this problem is related to the fact that the vertices of the graph are partitioned into a certain number of clusters and we are interested in finding a minimum-cost tree spanning a subset of vertices with precisely one vertex considered from every cluster. The paper is structured around the following main headings: problem definition, variations and practical applications, complexity aspects, integer programming formulations, exact and heuristic solution approaches developed for solving this problem. Furthermore, we also discuss some open problems and possible research directions.

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  • Pop, Petrică C., 2020. "The generalized minimum spanning tree problem: An overview of formulations, solution procedures and latest advances," European Journal of Operational Research, Elsevier, vol. 283(1), pages 1-15.
    • Handle: RePEc:eee:ejores:v:283:y:2020:i:1:p:1-15
    DOI: 10.1016/j.ejor.2019.05.017
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    1. José-Manuel Giménez-Gómez & Josep E Peris & Begoña Subiza, 2020. "An egalitarian approach for sharing the cost of a spanning tree," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-14, July.
    2. Jann Michael Weinand & Kenneth Sorensen & Pablo San Segundo & Max Kleinebrahm & Russell McKenna, 2020. "Research trends in combinatorial optimisation," Papers 2012.01294, arXiv.org.
    3. Pop, Petrică C. & Cosma, Ovidiu & Sabo, Cosmin & Sitar, Corina Pop, 2024. "A comprehensive survey on the generalized traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 314(3), pages 819-835.
    4. Gerson N. Cardoso & Geraldo E. Silva, 2024. "Electoral influences on the Brazilian B3 data correlation network," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 251-272, January.
    5. Yuriy Shablya & Dmitry Kruchinin & Vladimir Kruchinin, 2020. "Method for Developing Combinatorial Generation Algorithms Based on AND/OR Trees and Its Application," Mathematics, MDPI, vol. 8(6), pages 1-21, June.
    6. Cosmin Sabo & Petrică C. Pop & Andrei Horvat-Marc, 2020. "On the Selective Vehicle Routing Problem," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    7. Ana Klobučar & Robert Manger, 2020. "Solving Robust Variants of the Maximum Weighted Independent Set Problem on Trees," Mathematics, MDPI, vol. 8(2), pages 1-16, February.

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