Advertisement

Critical Node Detection with Connectivity Based on Bounded Path Lengths

  • Fábio BarbosaEmail author
  • Agostinho Agra
  • Amaro de Sousa
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 278)

Abstract

For a given graph representing a transparent optical network, a given weight associated to each node pair and a given positive integer c, the Critical Node Detection problem variant addressed here is the determination of the set of c nodes that, if removed from the graph, minimizes the total weight of the node pairs that remain connected. In the context of transparent optical networks, a node pair is considered connected only if the surviving network provides it with a shortest path not higher than a given positive value T representing the optical transparent reach of the network. Moreover, the length of a path depends both on the length of its links and on its number of intermediate nodes. A path-based Integer Linear Programming model is presented together with a row generation approach to solve it. We present computational results for a real-world network topology with 50 nodes and 88 links and for \(c=2\) up to 6. The optimal results are compared with node centrality based heuristics showing that such approaches provide solutions which are far from optimal.

Keywords

Critical node detection Transparent optical networks Path model Decomposition approach 

Notes

Acknowledgements

This article is based upon work from COST Action CA15127 (“Resilient communication services protecting end-user applications from disaster-based failures—RECODIS”), supported by COST (European Cooperation in Science and Technology), and from project CENTRO-01-0145-FEDER-029312 (ResNeD) supported by FEDER Funds and National Funds through FCT (Fundação para a Ciência e a Tecnologia), Portugal. First author was supported by FCT through Ph.D. grant SFRH/BD/132650/2017. Second author was supported by FCT through CIDMA within project UID/MAT/04106/2013.

References

  1. 1.
    Arulselvan, A., Commander, C.W., Elefteriadou, L., Pardalos, P.M.: Detecting critical nodes in sparse graphs. C&OR 36, 2193–2200 (2009)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Veremyev, A., Boginski, V., Pasiliao, E.: Exact identification of critical nodes in sparse networks via new compact formulations. Optim. Lett. 8, 1245–1259 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Di Summa, M., Grosso, A., Locatelli, M.: Branch and cut algorithms for detecting critical nodes in undirected graphs. Comput. Optim. Appl. 53(3), 649–680 (2012)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Santos, D., de Sousa, A., Monteiro, P.: Compact models for critical node detection in telecommunication networks. Electron. Notes Discret. Math. 64, 325–334 (2018)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Veremyev, A., Prokopyev, O., Pasiliao, E.: Critical nodes for distance-based connectivity and related problems in graphs. Networks 66(3), 170–195 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dinh, T., Xuan, Y., Thai, M., Pardalos, P., Znati, T.: On new approaches of assessing network vulnerability: hardness and approximation. IEEE/ACM Trans. Netw. 20(2), 609–619 (2012)CrossRefGoogle Scholar
  7. 7.
    Dinh, T., Thai, M.T.: Network under joint node and link attacks: vulnerability assessment methods and analysis. IEEE/ACM Trans. Netw. 23(3), 1001–1011 (2015)CrossRefGoogle Scholar
  8. 8.
    Rak, J., et al.: RECODIS: resilient communication services protecting end-user applications from disaster-based failures. In: Proceeding of ICTON, paper We.D1.4. (2016)Google Scholar
  9. 9.
    Gomes, T., et al.: A survey of strategies for communication networks to protect against large-scale natural disasters. In: Proceeding of RNDM, 2016, pp. 11–22 (2016)Google Scholar
  10. 10.
    Barbosa, F., de Sousa, A., Agra, A.: The design of transparent optical networks minimizing the impact of critical nodes. Electron. Notes Discret. Math. 64, 165–174 (2018)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Agra, A., de Sousa, A., Doostmohammadi, M.: The minimum cost design of transparent optical networks combining grooming, routing, and wavelength assignment. IEEE/ACM Tran. Netw. 24(6), 3702–3713 (2016)CrossRefGoogle Scholar
  12. 12.
    Orlowski, S., Wessaly, R., Pioro, M., Tomaszewski, A.: SNDlib 1.0 survivable network design library. Networks 55(3), 276–286 (2010)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Fábio Barbosa
    • 1
    Email author
  • Agostinho Agra
    • 2
  • Amaro de Sousa
    • 1
  1. 1.Instituto de Telecomunicações, Universidade de AveiroAveiroPortugal
  2. 2.CIDMA, Dept. MatemáticaUniversidade AveiroAveiroPortugal

Personalised recommendations