On the minimum diameter cost-constrained steiner tree problem

Wei Ding, Guoliang Xue

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

Given an edge-weighted undirected graph G = (V,E,c,w) where each edge e ∈ E has a cost c(e) ≥ 0 and another weight w(e) ≥ 0, a set S ⊆ V of terminals and a given constant C 0 ≥ 0, the aim is to find a minimum diameter Steiner tree whose all terminals appear as leaves and the cost of tree is bounded by C 0. The diameter of tree refers to the maximum weight of the paths connecting two different leaves in the tree. This problem is called the minimum diameter cost-constrained Steiner tree problem, which is NP-hard even when the topology of the Steiner tree is fixed. In this paper, we deal with the fixed-topology restricted version. We prove the restricted version to be polynomially solvable when the topology is not part of the input and propose a weakly fully polynomial time approximation scheme (weakly FPTAS) when the topology is part of the input, which can find a (1 + ε)-approximation of the restricted version problem for any ε > 0 with specific characteristic.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages37-48
Number of pages12
Volume7402 LNCS
DOIs
StatePublished - 2012
Event6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012 - Banff, AB, Canada
Duration: Aug 5 2012Aug 9 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7402 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012
CountryCanada
CityBanff, AB
Period8/5/128/9/12

Fingerprint

Steiner Tree Problem
Topology
Steiner Tree
Costs
Leaves
Fully Polynomial Time Approximation Scheme
Weighted Graph
Undirected Graph
NP-complete problem
Polynomials
Path
Approximation

Keywords

  • cost-constrained Steiner tree
  • fixed topology
  • Minimum diameter
  • weakly fully polynomial time approximation scheme

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Ding, W., & Xue, G. (2012). On the minimum diameter cost-constrained steiner tree problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7402 LNCS, pp. 37-48). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7402 LNCS). https://doi.org/10.1007/978-3-642-31770-5_4

On the minimum diameter cost-constrained steiner tree problem. / Ding, Wei; Xue, Guoliang.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7402 LNCS 2012. p. 37-48 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7402 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ding, W & Xue, G 2012, On the minimum diameter cost-constrained steiner tree problem. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7402 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7402 LNCS, pp. 37-48, 6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012, Banff, AB, Canada, 8/5/12. https://doi.org/10.1007/978-3-642-31770-5_4
Ding W, Xue G. On the minimum diameter cost-constrained steiner tree problem. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7402 LNCS. 2012. p. 37-48. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-31770-5_4
Ding, Wei ; Xue, Guoliang. / On the minimum diameter cost-constrained steiner tree problem. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7402 LNCS 2012. pp. 37-48 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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