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Finding the n Most Vital Links in Flow Networks

Author

Listed:
  • H. Donald Ratliff

    (University of Florida)

  • G. Thomas Sicilia

    (U.S. Army Military Personnel Center, Alexandria, Virginia)

  • S. H. Lubore

    (The Mitre Corporation, McLean, Virginia)

Abstract

The n most vital links of a flow network are defined as those n arcs whose simultaneous removal from the network causes the greatest decrease in the throughput capability of the remaining system between a specified pair of nodes. These n arcs are shown to be the n largest capacity arcs in a particular cut. A solution procedure is developed which involves sequentially modifying the network so as to make this cut eventually become the cut with smallest capacity. An algorithm with computational results is presented.

Suggested Citation

  • H. Donald Ratliff & G. Thomas Sicilia & S. H. Lubore, 1975. "Finding the n Most Vital Links in Flow Networks," Management Science, INFORMS, vol. 21(5), pages 531-539, January.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:5:p:531-539
    DOI: 10.1287/mnsc.21.5.531
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    Cited by:

    1. Gabriele Dragotto & Amine Boukhtouta & Andrea Lodi & Mehdi Taobane, 2024. "The critical node game," Journal of Combinatorial Optimization, Springer, vol. 47(5), pages 1-20, July.
    2. Alan Murray & Timothy Matisziw & Tony Grubesic, 2007. "Critical network infrastructure analysis: interdiction and system flow," Journal of Geographical Systems, Springer, vol. 9(2), pages 103-117, June.
    3. Oded Cats & Erik Jenelius, 2014. "Dynamic Vulnerability Analysis of Public Transport Networks: Mitigation Effects of Real-Time Information," Networks and Spatial Economics, Springer, vol. 14(3), pages 435-463, December.
    4. Khouzani, MHR. & Liu, Zhengliang & Malacaria, Pasquale, 2019. "Scalable min-max multi-objective cyber-security optimisation over probabilistic attack graphs," European Journal of Operational Research, Elsevier, vol. 278(3), pages 894-903.
    5. Tony H. Grubesic & Timothy C. Matisziw & Alan T. Murray & Diane Snediker, 2008. "Comparative Approaches for Assessing Network Vulnerability," International Regional Science Review, , vol. 31(1), pages 88-112, January.
    6. 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.
    7. Timothy Matisziw & Alan Murray & Tony Grubesic, 2009. "Exploring the vulnerability of network infrastructure to disruption," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 43(2), pages 307-321, June.
    8. Matthew Johnson & Alexander Gutfraind & Kiyan Ahmadizadeh, 2014. "Evader interdiction: algorithms, complexity and collateral damage," Annals of Operations Research, Springer, vol. 222(1), pages 341-359, November.
    9. Cristina Bazgan & Sonia Toubaline & Daniel Vanderpooten, 2013. "Critical edges/nodes for the minimum spanning tree problem: complexity and approximation," Journal of Combinatorial Optimization, Springer, vol. 26(1), pages 178-189, July.
    10. Rodríguez-Núñez, Eduardo & García-Palomares, Juan Carlos, 2014. "Measuring the vulnerability of public transport networks," Journal of Transport Geography, Elsevier, vol. 35(C), pages 50-63.
    11. 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.
    12. 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.
    13. 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.
    14. Alice Paul & Susan E. Martonosi, 2024. "The all-pairs vitality-maximization (VIMAX) problem," Annals of Operations Research, Springer, vol. 338(2), pages 1019-1048, July.
    15. Kosanoglu, Fuat & Bier, Vicki M., 2020. "Target-oriented utility for interdiction of transportation networks," Reliability Engineering and System Safety, Elsevier, vol. 197(C).

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