Journal of Combinatorial Optimization

, Volume 26, Issue 1, pp 178–189 | Cite as

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

  • Cristina Bazgan
  • Sonia Toubaline
  • Daniel Vanderpooten
Article

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 n1−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.

Keywords

Most vital edges/nodes Min edge/node blocker Minimum spanning tree Complexity Approximation 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Cristina Bazgan
    • 1
    • 2
  • Sonia Toubaline
    • 1
  • Daniel Vanderpooten
    • 1
  1. 1.LAMSADEUniversité Paris-DauphineParis Cedex 16France
  2. 2.Institut Universitaire de FranceParisFrance

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