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Annals of Operations Research

, Volume 238, Issue 1–2, pp 315–328 | Cite as

An estimate of the objective function optimum for the network Steiner problem

  • V. Kirzhner
  • Z. Volkovich
  • E. Ravve
  • G.-W. Weber
Article

Abstract

A complete weighted graph, \(G(X,\varGamma ,W)\), is considered. Let \(\tilde{X}\subset X\) be some subset of vertices and, by definition, a Steiner tree is any tree in the graph G such that the set of the tree vertices includes set \(\tilde{X}\). The Steiner tree problem consists of constructing the minimum-length Steiner tree in graph G, for a given subset of vertices \(\tilde{X}\) The effectively computable estimate of the minimal Steiner tree is obtained in terms of the mean value and the variance over the set of all Steiner trees. It is shown that in the space of the lengths of the graph edges, there exist some regions where the obtained estimate is better than the minimal spanning tree-based one.

Keywords

Spanning tree Steiner tree Steiner problem 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. Kirzhner
    • 1
  • Z. Volkovich
    • 2
  • E. Ravve
    • 2
  • G.-W. Weber
    • 3
    • 4
    • 5
    • 6
    • 7
  1. 1.Institute of EvolutionUniversity of HaifaHaifaIsrael
  2. 2.Ort Braude College of EngineeringKarmielIsrael
  3. 3.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  4. 4.University of SiegenSiegenGermany
  5. 5.University of AveiroAveiroPortugal
  6. 6.Universiti Teknologi MalaysiaSkudaiMalaysia
  7. 7.University of BallaratBallaratAustralia

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