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Interdicting facilities in tree networks

Author

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  • Nicolas Fröhlich

    (Technische Universität Kaiserslautern)

  • Stefan Ruzika

    (Technische Universität Kaiserslautern)

Abstract

This article investigates a network interdiction problem on a tree network: given a subset of nodes chosen as facilities, an interdictor may dissect the network by removing a size-constrained set of edges, striving to worsen the established facilities best possible. Here, we consider a reachability objective function, which is closely related to the covering objective function: the interdictor aims to minimize the number of customers that are still connected to any facility after interdiction. For the covering objective on general graphs, this problem is known to be NP-complete (Fröhlich and Ruzika In: On the hardness of covering-interdiction problems. Theor. Comput. Sci., 2021). In contrast to this, we propose a polynomial-time solution algorithm to solve the problem on trees. The algorithm is based on dynamic programming and reveals the relation of this location-interdiction problem to knapsack-type problems. However, the input data for the dynamic program must be elaborately generated and relies on the theoretical results presented in this article. As a result, trees are the first known graph class that admits a polynomial-time algorithm for edge interdiction problems in the context of facility location planning.

Suggested Citation

  • Nicolas Fröhlich & Stefan Ruzika, 2022. "Interdicting facilities in tree networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 95-118, April.
    • Handle: RePEc:spr:topjnl:v:30:y:2022:i:1:d:10.1007_s11750-021-00600-6
    DOI: 10.1007/s11750-021-00600-6
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    References listed on IDEAS

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    1. Smith, J. Cole & Song, Yongjia, 2020. "A survey of network interdiction models and algorithms," European Journal of Operational Research, Elsevier, vol. 283(3), pages 797-811.
    2. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    3. Scaparra, Maria P. & Church, Richard L., 2008. "An exact solution approach for the interdiction median problem with fortification," European Journal of Operational Research, Elsevier, vol. 189(1), pages 76-92, August.
    4. Andrea Baggio & Margarida Carvalho & Andrea Lodi & Andrea Tramontani, 2021. "Multilevel Approaches for the Critical Node Problem," Operations Research, INFORMS, vol. 69(2), pages 486-508, March.
    5. Leonardo Lozano & J. Cole Smith, 2017. "A Backward Sampling Framework for Interdiction Problems with Fortification," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 123-139, February.
    6. Ramamoorthy, Prasanna & Jayaswal, Sachin & Sinha, Ankur & Vidyarthi, Navneet, 2018. "Multiple allocation hub interdiction and protection problems: Model formulations and solution approaches," European Journal of Operational Research, Elsevier, vol. 270(1), pages 230-245.
    7. Drexl, Michael & Schneider, Michael, 2015. "A survey of variants and extensions of the location-routing problem," European Journal of Operational Research, Elsevier, vol. 241(2), pages 283-308.
    8. Kalcsics, Jörg & Nickel, Stefan & Pozo, Miguel A. & Puerto, Justo & Rodríguez-Chía, Antonio M., 2014. "The multicriteria p-facility median location problem on networks," European Journal of Operational Research, Elsevier, vol. 235(3), pages 484-493.
    9. Cristina Bazgan & Sonia Toubaline & Daniel Vanderpooten, 2013. "Complexity of determining the most vital elements for the p-median and p-center location problems," Journal of Combinatorial Optimization, Springer, vol. 25(2), pages 191-207, February.
    10. Ghaffarinasab, Nader & Atayi, Reza, 2018. "An implicit enumeration algorithm for the hub interdiction median problem with fortification," European Journal of Operational Research, Elsevier, vol. 267(1), pages 23-39.
    11. Maryam Soleimani-Alyar & Alireza Ghaffari-Hadigheh & Fatemeh Sadeghi, 2016. "Controlling Floods by Optimization Methods," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(12), pages 4053-4062, September.
    12. Furini, Fabio & Ljubić, Ivana & Martin, Sébastien & San Segundo, Pablo, 2019. "The maximum clique interdiction problem," European Journal of Operational Research, Elsevier, vol. 277(1), pages 112-127.
    13. Belarmino Adenso-Díaz & Julio Mar-Ortiz & Sebastián Lozano, 2018. "Assessing supply chain robustness to links failure," International Journal of Production Research, Taylor & Francis Journals, vol. 56(15), pages 5104-5117, August.
    14. Deniz Aksen & Nuray Piyade & Necati Aras, 2010. "The budget constrained r-interdiction median problem with capacity expansion," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 269-291, September.
    15. Streib, Lucas & Kattwinkel, Mira & Heer, Henriette & Ruzika, Stefan & Schäfer, Ralf B., 2020. "How does habitat connectivity influence the colonization success of a hemimetabolous aquatic insect? - A modeling approach," Ecological Modelling, Elsevier, vol. 416(C).
    16. Emilio Carrizosa & Stefan Nickel, 2003. "Robust facility location," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 331-349, November.
    Full references (including those not matched with items on IDEAS)

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