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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. Ioannis Gamvros & Bruce Golden & S. Raghavan & Daliborka Stanojević, 2005. "Heuristic Search for Network Design," International Series in Operations Research & Management Science, in: H J. G (ed.), Tutorials on Emerging Methodologies and Applications in Operations Research, chapter 0, pages 1-1-1-46, Springer.
    2. Moshe Dror & Mohamed Haouari, 2000. "Generalized Steiner Problems and Other Variants," Journal of Combinatorial Optimization, Springer, vol. 4(4), pages 415-436, December.
    3. Ghiani, Gianpaolo & Improta, Gennaro, 2000. "An efficient transformation of the generalized vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 122(1), pages 11-17, April.
    4. P. Pop, 2007. "On the prize-collecting generalized minimum spanning tree problem," Annals of Operations Research, Springer, vol. 150(1), pages 193-204, March.
    5. Miranda, Pablo A. & Blazquez, Carola A. & Obreque, Carlos & Maturana-Ross, Javier & Gutierrez-Jarpa, Gabriel, 2018. "The bi-objective insular traveling salesman problem with maritime and ground transportation costs," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1014-1036.
    6. Yagiura, Mutsunori & Ibaraki, Toshihide & Glover, Fred, 2006. "A path relinking approach with ejection chains for the generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 169(2), pages 548-569, March.
    7. Demange, Marc & Ekim, Tınaz & Ries, Bernard & Tanasescu, Cerasela, 2015. "On some applications of the selective graph coloring problem," European Journal of Operational Research, Elsevier, vol. 240(2), pages 307-314.
    8. Haouari, Mohamed & Chaouachi, Jouhaina Siala, 2006. "Upper and lower bounding strategies for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 171(2), pages 632-647, June.
    9. Pop, Petrică C. & Matei, Oliviu & Sabo, Cosmin & Petrovan, Adrian, 2018. "A two-level solution approach for solving the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 478-487.
    10. Stutzle, Thomas, 2006. "Iterated local search for the quadratic assignment problem," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1519-1539, November.
    11. Öncan, Temel & Cordeau, Jean-François & Laporte, Gilbert, 2008. "A tabu search heuristic for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 191(2), pages 306-319, December.
    12. Kansal, Anuraag R & Torquato, Salvatore, 2001. "Globally and locally minimal weight spanning tree networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 601-619.
    13. Feremans, Corinne & Labbe, Martine & Laporte, Gilbert, 2001. "On generalized minimum spanning trees," European Journal of Operational Research, Elsevier, vol. 134(2), pages 457-458, October.
    14. Pop, Petrica C. & Kern, W. & Still, G., 2006. "A new relaxation method for the generalized minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 170(3), pages 900-908, May.
    15. M Haouari & J Chaouachi & M Dror, 2005. "Solving the generalized minimum spanning tree problem by a branch-and-bound algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 382-389, April.
    16. Bruce Golden & S. Raghavan & Daliborka Stanojević, 2005. "Heuristic Search for the Generalized Minimum Spanning Tree Problem," INFORMS Journal on Computing, INFORMS, vol. 17(3), pages 290-304, August.
    17. Hintsch, Timo & Irnich, Stefan, 2018. "Large multiple neighborhood search for the clustered vehicle-routing problem," European Journal of Operational Research, Elsevier, vol. 270(1), pages 118-131.
    18. Dror, M. & Haouari, M. & Chaouachi, J., 2000. "Generalized spanning trees," European Journal of Operational Research, Elsevier, vol. 120(3), pages 583-592, February.
    19. Matteo Fischetti & Juan José Salazar González & Paolo Toth, 1997. "A Branch-and-Cut Algorithm for the Symmetric Generalized Traveling Salesman Problem," Operations Research, INFORMS, vol. 45(3), pages 378-394, June.
    20. Duin, C. W. & Volgenant, A. & Vo[ss], S., 2004. "Solving group Steiner problems as Steiner problems," European Journal of Operational Research, Elsevier, vol. 154(1), pages 323-329, April.
    21. Feremans, Corinne & Labbe, Martine & Laporte, Gilbert, 2003. "Generalized network design problems," European Journal of Operational Research, Elsevier, vol. 148(1), pages 1-13, July.
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    Cited by:

    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. 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.
    3. Cosmin Sabo & Petrică C. Pop & Andrei Horvat-Marc, 2020. "On the Selective Vehicle Routing Problem," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    4. Jann Michael Weinand & Kenneth Sorensen & Pablo San Segundo & Max Kleinebrahm & Russell McKenna, 2020. "Research trends in combinatorial optimisation," Papers 2012.01294, arXiv.org.
    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. 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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