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Analysis of Critical Damage in the Communication Network: III. Analysis of Internode Flows

  • MATHEMATICAL MODELING
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Journal of Computer and Systems Sciences International Aims and scope

Abstract

Changes in the values of the maximal permissible flows that can be transmitted between nodes in the case of network damage are analyzed through computational experiments. At the initial stage, the maximal single-product flow is independently determined for each pair of source–sink vertices. The maximal flow vector is used to estimate the functional capability limit of the original, intact network. In the course of computational experiments, each damage from the given set is considered sequentially; for all source–sink pairs, the maximal flows in the damaged network are found. For each pair of nodes, all damage are determined for which the maximal flow is either zero or less than the permissible value. Based on the data obtained, diagrams of possible damage for all pairs of source–sink are formed. Computational experiments are carried out for networks with radial-ring structures and coincident sets of nodes. The resulting diagrams allow us to compare and find the most vulnerable pairs with nondominated vector damage estimates.

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REFERENCES

  1. Yu. E. Malashenko and I. A. Nazarova, “Analysis of critical damage in the communication network. I. Model and computational experiment,” J. Comput. Syst. Sci. Int. 59, 745 (2020).

    Article  Google Scholar 

  2. Yu. E. Malashenko and I. A. Nazarova, “Analysis of critical damage in the communication network. II. Guaranteed functional performance estimates,” J. Comput. Syst. Sci. Int. 59, 918 (2020).

    Article  Google Scholar 

  3. Yu. B. Germeier, Introduction to the Theory of Operations Research (Nauka, Moscow, 1971) [in Russian].

    Google Scholar 

  4. J. M. Danskin, The Theory of Max-Min and its Application to Weapons Allocation Problems (Springer, Berlin, 1967).

    Book  Google Scholar 

  5. J. J. Cochran, L. A. Cox, Jr., P. Keskinocak, et al., Wiley Encyclopedia of Operations Research and Management Science (Wiley, New York, 2010).

    Book  Google Scholar 

  6. Yu. E. Malashenko, I. A. Nazarova, and N. M. Novikova, “Express analysis and aggregated representation of the set of reachable flows for a multicommodity network system,” J. Comput. Syst. Sci. Int. 58, 889 (2019).

    Article  Google Scholar 

  7. P. Jensen and W. J. Barnes, Network Flow Programming (Wiley, New York, 1980).

    MATH  Google Scholar 

  8. T. H. Grubesic, T. C. Matisziw, A. T. Murray, et al., “Comparative approaches for assessing network vulnerability,” Int. Region. Sci. Rev. 31, 88 (2008).

    Article  Google Scholar 

  9. A. T. Murray, “An overview of network vulnerability modeling approaches,” Geo J. 78, 209–221 (2013).

    Google Scholar 

  10. J. Johansson, “Risk and vulnerability analysis of interdependent technical infrastructures. Addressing sociotechnical systems,” Doctoral Thesis (Lund Univ., Lund, 2010).

  11. T. Gomes, C. Esposito, D. Hutchison, et al., “Survey of strategies for communication networks to protect against large-scale natural disasters,” in Proceedings of the International Workshop on Reliable Networks Design and Modeling RNDM, Halmstad, 2016, pp. 11–22.

  12. J. O. Royset and R. K. Wood, “Solving the bi-objective maximum-flow network-interdiction problem,” INFORMS J. Comput. 19, 175–184 (2007).

    Article  MathSciNet  Google Scholar 

  13. J. Walteros and P. Pardalos, “Selected topics in critical element detection,” Optimiz. Appl. 71, 9–26 (2012).

    MathSciNet  MATH  Google Scholar 

  14. Yu. E. Malashenko, I. A. Nazarova, and N. M. Novikova, “An approach to the analysis of possible structural damages in multicommodity network systems,” Comput. Math. Math. Phys. 59, 1562 (2019).

    Article  MathSciNet  Google Scholar 

  15. A. Veremyev, O. A. Prokipyev, and E. L. Pasiliao, “Critical nodes for distance-based connectivity and related problems in graphs,” Networks 66, 170–195 (2015).

    Article  MathSciNet  Google Scholar 

  16. M. Ventresca, K. R. Harrison, and B. M. Ombuki-Berman, “The bi-objective critical node detection problem,” Eur. J. Oper. Res. 265, 895–908 (2018).

    Article  MathSciNet  Google Scholar 

  17. J. Li, P. M. Pardalos, B. Xin, and J. Chen, “The bi-objective critical node detection problem with minimum pairwise connectivity and cost: Theory and algorithms,” Soft Comput. 23, 1–16 (2019).

    Article  Google Scholar 

  18. M. Lalou, M. A. Tahraoui, and H. Kheddouci, “The critical node detection problem in networks: A survey,” Comput. Sci. Rev. 28, 92–117 (2018).

    Article  MathSciNet  Google Scholar 

  19. A. Kuhnle, N. P. Nguyen, T. N. Dinh, et al., “Vulnerability of clustering under nodes failure in complex networks,” Social Network Anal. Mining 7, 8–24 (2017).

    Article  Google Scholar 

  20. Yu. E. Malashenko, I. A. Nazarova, and N. M. Novikova, “Analysis of cluster damages in network systems,” Comput. Math. Math. Phys. 60, 341 (2020).

    Article  MathSciNet  Google Scholar 

  21. Th. H. Cormen, Ch. Leiserson, R. L. Rivest, et al., Introduction to Algorithms, 3rd ed. (MIT Press, Cambridge, MA, 2009).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, 119333, Moscow, Russia

    Y. E. Malashenko & I. A. Nazarova

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  1. Y. E. Malashenko
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  2. I. A. Nazarova
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Correspondence to I. A. Nazarova.

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Malashenko, Y.E., Nazarova, I.A. Analysis of Critical Damage in the Communication Network: III. Analysis of Internode Flows. J. Comput. Syst. Sci. Int. 60, 576–584 (2021). https://doi.org/10.1134/S1064230721030102

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  • DOI: https://doi.org/10.1134/S1064230721030102

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