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

Kirzhner V., Volkovich Z., Ravve E., Weber G. -.

ANNALS OF OPERATIONS RESEARCH, vol.238, pp.315-328, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 238
  • Publication Date: 2016
  • Doi Number: 10.1007/s10479-015-2068-1
  • Journal Name: ANNALS OF OPERATIONS RESEARCH
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.315-328
  • Keywords: Spanning tree, Steiner tree, Steiner problem
  • Middle East Technical University Affiliated: Yes

Abstract

A complete weighted graph, G(X, Gamma, W), is considered. Let (X) over tilde subset of 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 (X) over tilde. The Steiner tree problem consists of constructing the minimum-length Steiner tree in graph G, for a given subset of vertices (X) over tilde 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.