Branch and cut algorithms for detecting critical nodes in undirected graphs

Marco Di Summa (), Andrea Grosso () and Marco Locatelli ()

Computational Optimization and Applications, 2012, vol. 53, issue 3, 649-680

Abstract: In this paper we deal with the critical node problem, where a given number of nodes has to be removed from an undirected graph in order to maximize the disconnections between the node pairs of the graph. We propose an integer linear programming model with a non-polynomial number of constraints but whose linear relaxation can be solved in polynomial time. We derive different valid inequalities and some theoretical results about them. We also propose an alternative model based on a quadratic reformulation of the problem. Finally, we perform many computational experiments and analyze the corresponding results. Copyright Springer Science+Business Media, LLC 2012

Keywords: Critical node problem; Branch and cut; Valid inequalities; Reformulation-linearization technique (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (21)

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DOI: 10.1007/s10589-012-9458-y

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