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Critical edges/nodes for the minimum spanning tree problem: complexity and approximation

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Abstract

In this paper, we study the complexity and the approximation of the k most vital edges (nodes) and min edge (node) blocker versions for the minimum spanning tree problem (MST). We show that the k most vital edges MST problem is NP-hard even for complete graphs with weights 0 or 1 and 3-approximable for graphs with weights 0 or 1. We also prove that the k most vital nodes MST problem is not approximable within a factor n 1−ϵ, for any ϵ>0, unless NP=ZPP, even for complete graphs of order n with weights 0 or 1. Furthermore, we show that the min edge blocker MST problem is NP-hard even for complete graphs with weights 0 or 1 and that the min node blocker MST problem is NP-hard to approximate within a factor 1.36 even for graphs with weights 0 or 1.

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Authors and Affiliations

  1. LAMSADE, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Cristina Bazgan, Sonia Toubaline & Daniel Vanderpooten

  2. Institut Universitaire de France, Paris, France

    Cristina Bazgan

Authors
  1. Cristina Bazgan
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  2. Sonia Toubaline
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  3. Daniel Vanderpooten
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Correspondence to Cristina Bazgan.

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Bazgan, C., Toubaline, S. & Vanderpooten, D. Critical edges/nodes for the minimum spanning tree problem: complexity and approximation. J Comb Optim 26, 178–189 (2013). https://doi.org/10.1007/s10878-011-9449-4

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  • DOI: https://doi.org/10.1007/s10878-011-9449-4

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