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Cardinality-Constrained Critical Node Detection Problem

In: Performance Models and Risk Management in Communications Systems

Author

Listed:
  • Ashwin Arulselvan

    (University of Warwick)

  • Clayton W. Commander

    (University of Florida)

  • Oleg Shylo

    (University of Florida)

  • Panos M. Pardalos

    (University of Florida)

Abstract

We consider methodologies for managing risk in a telecommunication network based on identification of the critical nodes. The objective is to minimize the number of vertices whose deletion results in disconnected components which are constrained by a given cardinality. This is referred to as the CARDINALITY CONSTRAINED CRITICAL NODE PROBLEM (CC-CNP), and finds application in epidemic control, telecommunications, and military tactical planning, among others. From a telecommunication perspective, the set of critical nodes helps determine which players should be removed from the network in the event of a virus outbreak. Conversely, in order to maintain maximum global connectivity, it should be ensured that the critical nodes remain intact and as secure as possible. The presence of these nodes make a network vulnerable to attacks as they are crucial for the overall connectivity. This is a variation of the CRITICAL NODE DETECTION PROBLEM which has a known complexity and heuristic procedure. In this chapter, we review the recent work in this area, provide formulations based on integer linear programming and develop heuristic procedures for CC-CNP. We also examine the relations of CC-CNP with the well known NODE DELETION PROBLEM and discuss complexity results as a result of this relation.

Suggested Citation

  • Ashwin Arulselvan & Clayton W. Commander & Oleg Shylo & Panos M. Pardalos, 2011. "Cardinality-Constrained Critical Node Detection Problem," Springer Optimization and Its Applications, in: Nalân Gülpınar & Peter Harrison & Berç Rüstem (ed.), Performance Models and Risk Management in Communications Systems, pages 79-91, Springer.
    • Handle: RePEc:spr:spochp:978-1-4419-0534-5_4
    DOI: 10.1007/978-1-4419-0534-5_4
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    Citations

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    Cited by:

    1. Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2014. "An integer programming framework for critical elements detection in graphs," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 233-273, July.
    2. Joe Naoum-Sawaya & Christoph Buchheim, 2016. "Robust Critical Node Selection by Benders Decomposition," INFORMS Journal on Computing, INFORMS, vol. 28(1), pages 162-174, February.
    3. Gokhan Karakose & Ronald G. McGarvey, 2019. "Optimal Detection of Critical Nodes: Improvements to Model Structure and Performance," Networks and Spatial Economics, Springer, vol. 19(1), pages 1-26, March.
    4. Faramondi, Luca & Setola, Roberto & Panzieri, Stefano & Pascucci, Federica & Oliva, Gabriele, 2018. "Finding critical nodes in infrastructure networks," International Journal of Critical Infrastructure Protection, Elsevier, vol. 20(C), pages 3-15.
    5. Zhang, Yifan & Ng, S. Thomas, 2021. "A hypothesis-driven framework for resilience analysis of public transport network under compound failure scenarios," International Journal of Critical Infrastructure Protection, Elsevier, vol. 35(C).
    6. Veremyev, Alexander & Sorokin, Alexey & Boginski, Vladimir & Pasiliao, Eduardo L., 2014. "Minimum vertex cover problem for coupled interdependent networks with cascading failures," European Journal of Operational Research, Elsevier, vol. 232(3), pages 499-511.

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