Skip to main content

An Extremal Optimization Approach to the Pairwise Connectivity Critical Node Detection Problem

  • Conference paper
  • First Online:
17th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2022) (SOCO 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 531))

  • 518 Accesses

Abstract

The critical node detection is a computational challenging problem with several applications in biology, sociology, etc. Minimizing the pairwise connectivity after removing k critical nodes is one of the most studied problem. In this paper we approach this problem by using a standard Extremal Optimization algorithm, and another variant with incorporated network shifting mechanism. Network centrality measures are used to speed up the search, the variants are analyzed on synthetic and real-world problems. Numerical results indicate the potential of the proposed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Downloaded from http://individual.utoronto.ca/mventresca/cnd.html.

  2. 2.

    Downloaded from https://networkrepository.com/.

References

  1. Aringhieri, R., Grosso, A., Hosteins, P., Scatamacchia, R.: A general evolutionary framework for different classes of critical node problems. Eng. Appl. Artif. Intell. 55, 128–145 (2016)

    Article  Google Scholar 

  2. Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardalos, P.M.: Detecting critical nodes in sparse graphs. Comput. Oper. Res. 36(7), 2193–2200 (2009)

    Article  MathSciNet  Google Scholar 

  3. Arulselvan, A., Commander, C.W., Pardalos, P.M., Shylo, O.: Managing network risk via critical node identification. Risk management in telecommunication networks. Springer (2007)

    Google Scholar 

  4. Arulselvan, A., Commander, C.W., Shylo, O., Pardalos, P.M.: Cardinality-constrained critical node detection problem. In: Gülpınar, N., Harrison, P., Rüstem, B. (eds.) Performance Models and Risk Management in Communications Systems. SOIA, vol. 46, pp. 79–91. Springer, New York (2011). https://doi.org/10.1007/978-1-4419-0534-5_4

    Chapter  Google Scholar 

  5. Barabási, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)

    Article  MathSciNet  Google Scholar 

  6. Boettcher, S., Percus, A.G.: Optimization with extremal dynamics. Phys. Rev. Lett. 86, 5211–5214 (2001)

    Article  Google Scholar 

  7. Boettcher, S., Percus, A.G.: Extremal optimization: an evolutionary local-search algorithm. In: Bhargava, H.K., Ye, N. (eds.) Computational Modeling and Problem Solving in the Networked World. Operations Research/Computer Science Interfaces Series, vol. 21, pp. 61–77. Springer, Heidelberg (2003). https://doi.org/10.1007/978-1-4615-1043-7_3

  8. Borgatti, S.P.: Identifying sets of key players in a social network. Comput. Math. Organ. Theory 12(1), 21–34 (2006)

    Article  Google Scholar 

  9. Buluç, A., Meyerhenke, H., Safro, I., Sanders, P., Schulz, C.: Recent advances in graph partitioning. In: Kliemann, L., Sanders, P. (eds.) Algorithm Engineering. LNCS, vol. 9220, pp. 117–158. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49487-6_4

    Chapter  Google Scholar 

  10. Cacchiani, V., Caprara, A., Toth, P.: Scheduling extra freight trains on railway networks. Transp. Res. Part B Methodol. 44(2), 215–231 (2010)

    Article  Google Scholar 

  11. Chen, W., Wang, Y., Yang, S.: Efficient influence maximization in social networks. In: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 199–208 (2009)

    Google Scholar 

  12. Gaskó, N., Képes, T., Suciu, M., Lung, R.I.: Critical node detection for maximization of connected components: an extremal optimization approach. In: Sanjurjo González, H., Pastor López, I., García Bringas, P., Quintián, H., Corchado, E. (eds.) SOCO 2021. AISC, vol. 1401, pp. 502–511. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-87869-6_48

    Chapter  Google Scholar 

  13. He, J., Liang, H., Yuan, H.: Controlling infection by blocking nodes and links simultaneously. In: Chen, N., Elkind, E., Koutsoupias, E. (eds.) WINE 2011. LNCS, vol. 7090, pp. 206–217. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25510-6_18

    Chapter  Google Scholar 

  14. Iyer, S., Killingback, T., Sundaram, B., Wang, Z.: Attack robustness and centrality of complex networks. PLoS ONE 8(4), e59613 (2013)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  16. Lewis, J.M., Yannakakis, M.: The node-deletion problem for hereditary properties is NP-complete. J. Comput. Syst. Sci. 20(2), 219–230 (1980)

    Article  MathSciNet  Google Scholar 

  17. Lozano, M., García-Martínez, C., Rodriguez, F.J., Trujillo, H.M.: Optimizing network attacks by artificial bee colony. Inf. Sci. 377, 30–50 (2017)

    Article  Google Scholar 

  18. Lung, R.I., Suciu, M., Gaskó, N.: Noisy extremal optimization. Soft. Comput. 21(5), 1253–1270 (2017)

    Article  Google Scholar 

  19. Milo, R., et al.: Superfamilies of evolved and designed networks. Science 303(5663), 1538–1542 (2004)

    Article  Google Scholar 

  20. Purevsuren, D., Cui, G., Win, N.N.H., Wang, X.: Heuristic algorithm for identifying critical nodes in graphs. Adv. Comput. Sci. Int. J. 5(3), 1–4 (2016)

    Google Scholar 

  21. Reimand, J., Tooming, L., Peterson, H., Adler, P., Vilo, J.: GraphWeb: mining heterogeneous biological networks for gene modules with functional significance. Nucleic Acids Res. 36, 452–459 (2008)

    Google Scholar 

  22. Rossi, R.A., Ahmed, N.K.: The network data repository with interactive graph analytics and visualization. In: AAAI (2015)

    Google Scholar 

  23. Ventresca, M.: Global search algorithms using a combinatorial unranking-based problem representation for the critical node detection problem. Comput. Oper. Res. 39(11), 2763–2775 (2012)

    Article  MathSciNet  Google Scholar 

  24. Ventresca, M., Harrison, K.R., Ombuki-Berman, B.M.: The bi-objective critical node detection problem. Eur. J. Oper. Res. 265(3), 895–908 (2018)

    Article  MathSciNet  Google Scholar 

  25. Veremyev, A., Prokopyev, O.A., Pasiliao, E.L.: An integer programming framework for critical elements detection in graphs. J. Comb. Optim. 28(1), 233–273 (2014)

    Article  MathSciNet  Google Scholar 

  26. Veremyev, A., Prokopyev, O.A., Pasiliao, E.L.: Critical nodes for distance-based connectivity and related problems in graphs. Networks 66(3), 170–195 (2015)

    Article  MathSciNet  Google Scholar 

  27. Watts, A.: A dynamic model of network formation. Games Econom. Behav. 34(2), 331–341 (2001)

    Article  MathSciNet  Google Scholar 

  28. Yang, R., Huang, L., Lai, Y.C.: Selectivity-based spreading dynamics on complex networks. Phys. Rev. E 78(2), 026111 (2008)

    Article  Google Scholar 

  29. Zhou, Y., Hao, J.K., Glover, F.: Memetic search for identifying critical nodes in sparse graphs. IEEE Trans. Cybern. 49(10), 3699–3712 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS - UEFISCDI, project number PN-III-P1-1.1-TE-2019-1633.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Noémi Gaskó .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gaskó, N., Képes, T., Suciu, M., Lung, R.I. (2023). An Extremal Optimization Approach to the Pairwise Connectivity Critical Node Detection Problem. In: García Bringas, P., et al. 17th International Conference on Soft Computing Models in Industrial and Environmental Applications (SOCO 2022). SOCO 2022. Lecture Notes in Networks and Systems, vol 531. Springer, Cham. https://doi.org/10.1007/978-3-031-18050-7_11

Download citation

Publish with us

Policies and ethics