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

  • Mohammed Lalou
  • Hamamache Kheddouci
Original Paper


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.


Critical nodes Graph connectivity Bipartite permutation graphs Dynamic programming Complete bipartite decomposition Graph separators 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université Claude Bernard Lyon 1, France - UFR-InformatiqueVilleurbanne CedexFrance
  2. 2.Institut des Sciences et TechnologieCentre Universitaire A. BoussoufMilaAlgeria
  3. 3.Département d’Informatique, Faculté des Sciences ExactesUniversité de BéjaiaBejaiaAlgeria

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