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A polynomial-time algorithm for finding critical nodes in bipartite permutation graphs

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Abstract

In this paper, we propose a polynomial-time algorithm for solving the Component-Cardinality-Constrained Critical Node Problem (3C-CNP) on bipartite permutation graphs. This problem, which is a variant of the well-known Critical Node Detection problem, consists in finding the minimal subset of nodes within a graph, the deletion of which results in a set of connected components of at most K nodes each one, where K is a given integer. The proposed algorithm is a dynamic programming scheme of time complexity \(O(nK^2)\), where n is the number of nodes. To provide evidences of algorithm’s efficiency, different experiments have been performed on randomly generated graphs.

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Notes

  1. Only the execution time of the equations is computed, without the time of loading data from files.

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Authors and Affiliations

  1. Université Claude Bernard Lyon 1, France - UFR-Informatique, Lab LIRIS 43 bd du 11 Novembre 1918, 69622, Villeurbanne Cedex, France

    Mohammed Lalou & Hamamache Kheddouci

  2. Institut des Sciences et Technologie, Centre Universitaire A. Boussouf, Mila, Algeria

    Mohammed Lalou

  3. Département d’Informatique, Faculté des Sciences Exactes, Université de Béjaia, Bejaia, Algeria

    Mohammed Lalou

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  1. Mohammed Lalou
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  2. Hamamache Kheddouci
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Correspondence to Mohammed Lalou.

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Lalou, M., Kheddouci, H. A polynomial-time algorithm for finding critical nodes in bipartite permutation graphs. Optim Lett 13, 1345–1364 (2019). https://doi.org/10.1007/s11590-018-1371-6

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