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)


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.


Critical node detection Transparent optical networks Path model Decomposition approach 



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.


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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

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