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Critical Node Detection with Connectivity Based on Bounded Path Lengths

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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

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  • DOI: 10.1007/978-3-030-10731-4_2
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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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Correspondence to Fábio Barbosa .

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Barbosa, F., Agra, A., de Sousa, A. (2019). Critical Node Detection with Connectivity Based on Bounded Path Lengths. In: Alves, M., Almeida, J., Oliveira, J., Pinto, A. (eds) Operational Research. IO 2018. Springer Proceedings in Mathematics & Statistics, vol 278. Springer, Cham.

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