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An integer programming framework for critical elements detection in graphs

Author

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  • Alexander Veremyev

    (Air Force Research Laboratory, Munitions Directorate)

  • Oleg A. Prokopyev

    (University of Pittsburgh)

  • Eduardo L. Pasiliao

    (Air Force Research Laboratory, Munitions Directorate)

Abstract

This study presents an integer programming framework for minimizing the connectivity and cohesiveness properties of a given graph by removing nodes and edges subject to a joint budgetary constraint. The connectivity and cohesiveness metrics are assumed to be general functions of sizes of the remaining connected components and node degrees, respectively. We demonstrate that our approach encompasses, as special cases (possibly, under some mild conditions), several other models existing in the literature, including minimization of the total number of connected node pairs, minimization of the largest connected component size, and maximization of the number of connected components. We discuss computational complexity issues, derive linear mixed integer programming (MIP) formulations, and describe additional modeling enhancements aimed at improving the performance of MIP solvers. We also conduct extensive computational experiments with real-life and randomly generated network instances under various settings that reveal interesting insights and demonstrate advantages and limitations of the proposed framework.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:28:y:2014:i:1:d:10.1007_s10878-014-9730-4
    DOI: 10.1007/s10878-014-9730-4
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    References listed on IDEAS

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    Cited by:

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    3. Mahdavi Pajouh, Foad & Walteros, Jose L. & Boginski, Vladimir & Pasiliao, Eduardo L., 2015. "Minimum edge blocker dominating set problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 16-26.
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    6. Marco Di Summa & Syed Md Omar Faruk, 2023. "Critical node/edge detection problems on trees," 4OR, Springer, vol. 21(3), pages 439-455, September.
    7. Lordan, Oriol & Albareda-Sambola, Maria, 2019. "Exact calculation of network robustness," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 276-280.
    8. Zhong, Haonan & Mahdavi Pajouh, Foad & A． Prokopyev, Oleg, 2023. "On designing networks resilient to clique blockers," European Journal of Operational Research, Elsevier, vol. 307(1), pages 20-32.
    9. 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.
    10. Hooshmand, F. & Mirarabrazi, F. & MirHassani, S.A., 2020. "Efficient Benders decomposition for distance-based critical node detection problem," Omega, Elsevier, vol. 93(C).
    11. 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.
    12. Matsypura, Dmytro & Prokopyev, Oleg A. & Zahar, Aizat, 2018. "Wildfire fuel management: Network-based models and optimization of prescribed burning," European Journal of Operational Research, Elsevier, vol. 264(2), pages 774-796.
    13. 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.
    14. 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).
    15. Alexander Veremyev & Konstantin Pavlikov & Eduardo L. Pasiliao & My T. Thai & Vladimir Boginski, 2019. "Critical nodes in interdependent networks with deterministic and probabilistic cascading failures," Journal of Global Optimization, Springer, vol. 74(4), pages 803-838, August.
    16. Ningji Wei & Jose L. Walteros & Foad Mahdavi Pajouh, 2021. "Integer Programming Formulations for Minimum Spanning Tree Interdiction," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1461-1480, October.
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    18. 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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