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

Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2013), Critical edges/nodes for the minimum spanning tree problem: complexity and approximation, Journal of Combinatorial Optimization, 26, 1, p. 178-189. 10.1007/s10878-011-9449-4

Type
Article accepté pour publication ou publié
Date
2013
Journal name
Journal of Combinatorial Optimization
Volume
26
Number
1
Publisher
Springer
Pages
178-189
Publication identifier
10.1007/s10878-011-9449-4
Metadata
Show full item record
Author(s)
Bazgan, Cristina
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Toubaline, Sónia
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Vanderpooten, Daniel
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
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.
Subjects / Keywords
Complexity; Approximation; Most vital edges/nodes; Minimum spanning tree; Min edge/node blocker

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    Efficient Algorithms for Finding the k Most Vital Edges for the Minimum Spanning Tree Problem 
    Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2011) Communication / Conférence
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    Complexity of determining the most vital elements for the 1-median and 1-center location problems 
    Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2010) Communication / Conférence
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    Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2013) Article accepté pour publication ou publié
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