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Selected Topics in Critical Element Detection

In: Applications of Mathematics and Informatics in Military Science

Author

Listed:
  • Jose L. Walteros

    (University of Florida)

  • Panos M. Pardalos

    (University of Florida)

Abstract

In this paper we consider the problem of detecting critical elements in networks. The objective of these problems is to identify a subset of elements (i.e., nodes, arcs, paths, cliques, etc.) whose deletion minimizes a given connectivity measure over the resulting network. This paper surveys some of the recent advances for solving these kinds of problems including heuristic, mathematical programming, approximated algorithms, and dynamic programming approaches.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:spochp:978-1-4614-4109-0_2
    DOI: 10.1007/978-1-4614-4109-0_2
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    Citations

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    Cited by:

    1. Huff, Johnathon D. & Leonard, William B. & Medal, Hugh R., 2022. "The wireless network jamming problem subject to protocol interference using directional antennas and with battery capacity constraints," International Journal of Critical Infrastructure Protection, Elsevier, vol. 39(C).
    2. Alexander Veremyev & Oleg A. Prokopyev & Eduardo L. Pasiliao, 2019. "Finding Critical Links for Closeness Centrality," INFORMS Journal on Computing, INFORMS, vol. 31(2), pages 367-389, April.
    3. 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.
    4. 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.
    5. 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).
    6. Balasundaram, Balabhaskar & Borrero, Juan S. & Pan, Hao, 2022. "Graph signatures: Identification and optimization," European Journal of Operational Research, Elsevier, vol. 296(3), pages 764-775.
    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.
    8. 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.
    9. Xing Zhou & Wei Peng & Zhen Xu & Bo Yang, 2015. "Hardness Analysis and Empirical Studies of the Relations among Robustness, Topology and Flow in Dynamic Networks," PLOS ONE, Public Library of Science, vol. 10(12), pages 1-29, December.

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