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

Cristina Bazgan (), Sonia Toubaline () and Daniel Vanderpooten ()
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Cristina Bazgan: Université Paris-Dauphine
Sonia Toubaline: Université Paris-Dauphine
Daniel Vanderpooten: Université Paris-Dauphine

Journal of Combinatorial Optimization, 2013, vol. 26, issue 1, No 14, 178-189

Abstract: 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.

Keywords: Most vital edges/nodes; Min edge/node blocker; Minimum spanning tree; Complexity; Approximation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10878-011-9449-4

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