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

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.