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 publiéDate
2013Journal name
Journal of Combinatorial OptimizationVolume
26Number
1Publisher
Springer
Pages
178-189
Publication identifier
Metadata
Show full item recordAuthor(s)
Bazgan, CristinaLaboratoire 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 blockerRelated items
Showing items related by title and author.
-
Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2011) Communication / Conférence
-
Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2012) Article accepté pour publication ou publié
-
Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2013) Article accepté pour publication ou publié
-
Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2010) Communication / Conférence
-
Bazgan, Cristina; Toubaline, Sónia; Vanderpooten, Daniel (2013) Article accepté pour publication ou publié