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Hybrid constructive heuristics for the critical node problem

Author

Listed:
  • Bernardetta Addis

    (Université de Lorraine, INRIA Nancy Grand Est)

  • Roberto Aringhieri

    (Università degli Studi di Torino)

  • Andrea Grosso

    (Università degli Studi di Torino)

  • Pierre Hosteins

    (Università degli Studi di Torino)

Abstract

We consider the Critical Node Problem: given an undirected graph and an integer number K, at most K nodes have to be deleted from the graph in order to minimize a connectivity measure in the residual graph. We combine the basic steps used in common greedy algorithms with some flavour of local search, in order to obtain simple hybrid heuristic algorithms. The obtained algorithms are shown to be effective, delivering improved performances (solution quality and speed) with respect to known greedy algorithms and other more sophisticated state of the art methods.

Suggested Citation

  • Bernardetta Addis & Roberto Aringhieri & Andrea Grosso & Pierre Hosteins, 2016. "Hybrid constructive heuristics for the critical node problem," Annals of Operations Research, Springer, vol. 238(1), pages 637-649, March.
    • Handle: RePEc:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-016-2110-y
    DOI: 10.1007/s10479-016-2110-y
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    References listed on IDEAS

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    1. Jose L. Walteros & Panos M. Pardalos, 2012. "Selected Topics in Critical Element Detection," Springer Optimization and Its Applications, in: Nicholas J. Daras (ed.), Applications of Mathematics and Informatics in Military Science, edition 127, chapter 0, pages 9-26, Springer.
    2. 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.
    3. Richard Wollmer, 1964. "Removing Arcs from a Network," Operations Research, INFORMS, vol. 12(6), pages 934-940, December.
    4. Marco Di Summa & Andrea Grosso & Marco Locatelli, 2012. "Branch and cut algorithms for detecting critical nodes in undirected graphs," Computational Optimization and Applications, Springer, vol. 53(3), pages 649-680, December.
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    Cited by:

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    2. Zhou, Yangming & Wang, Gezi & Hao, Jin-Kao & Geng, Na & Jiang, Zhibin, 2023. "A fast tri-individual memetic search approach for the distance-based critical node problem," European Journal of Operational Research, Elsevier, vol. 308(2), pages 540-554.
    3. Hosseinali Salemi & Austin Buchanan, 2022. "Solving the Distance-Based Critical Node Problem," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1309-1326, May.
    4. Chen, Wei & Jiang, Manrui & Jiang, Cheng & Zhang, Jun, 2020. "Critical node detection problem for complex network in undirected weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    5. Marco Di Summa & Syed Md Omar Faruk, 2023. "Critical node/edge detection problems on trees," 4OR, Springer, vol. 21(3), pages 439-455, September.
    6. Yibo Dong & Jin Liu & Jiaqi Ren & Zhe Li & Weili Li, 2023. "Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs," Mathematics, MDPI, vol. 11(24), pages 1-18, December.
    7. Ventresca, Mario & Harrison, Kyle Robert & Ombuki-Berman, Beatrice M., 2018. "The bi-objective critical node detection problem," European Journal of Operational Research, Elsevier, vol. 265(3), pages 895-908.

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