Approximations for Steiner Trees with Minimum Number of Steiner Points

Donghui Chen, Ding Zhu Du, Xiao Dong Hu, Guo Hui Lin, Lusheng Wang, Guoliang Xue

Research output: Contribution to journalArticle

111 Citations (Scopus)

Abstract

Given n terminals in the Euclidean plane and a positive constant, find a Steiner tree interconnecting all terminals with the minimum number of Steiner points such that the Euclidean length of each edge is no more than the given positive constant. This problem is NP-hard with applications in VLSI design, WDM optical networks and wireless communications. In this paper, we show that (a) the Steiner ratio is 1/4, that is, the minimum spanning tree yields a polynomial-time approximation with performance ratio exactly 4, (b) there exists a polynomial-time approximation with performance ratio 3, and (c) there exists a polynomial-time approximation scheme under certain conditions.

Original languageEnglish (US)
Pages (from-to)17-33
Number of pages17
JournalJournal of Global Optimization
Volume18
Issue number1
StatePublished - Sep 2000
Externally publishedYes

Fingerprint

Steiner Point
Steiner Tree
Polynomial time
Steiner Ratio
Polynomials
Optical Wireless
VLSI Design
WDM Networks
Polynomial Time Approximation Scheme
Network Communication
Euclidean plane
Optical Communication
Minimum Spanning Tree
Optical Networks
Approximation
Wireless Communication
Euclidean
NP-complete problem
Fiber optic networks
Wavelength division multiplexing

Keywords

  • Approximation algorithms
  • Steiner trees
  • VLSI design
  • WDM optical networks

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Global and Planetary Change
  • Applied Mathematics
  • Control and Optimization

Cite this

Chen, D., Du, D. Z., Hu, X. D., Lin, G. H., Wang, L., & Xue, G. (2000). Approximations for Steiner Trees with Minimum Number of Steiner Points. Journal of Global Optimization, 18(1), 17-33.

Approximations for Steiner Trees with Minimum Number of Steiner Points. / Chen, Donghui; Du, Ding Zhu; Hu, Xiao Dong; Lin, Guo Hui; Wang, Lusheng; Xue, Guoliang.

In: Journal of Global Optimization, Vol. 18, No. 1, 09.2000, p. 17-33.

Research output: Contribution to journalArticle

Chen, D, Du, DZ, Hu, XD, Lin, GH, Wang, L & Xue, G 2000, 'Approximations for Steiner Trees with Minimum Number of Steiner Points', Journal of Global Optimization, vol. 18, no. 1, pp. 17-33.
Chen, Donghui ; Du, Ding Zhu ; Hu, Xiao Dong ; Lin, Guo Hui ; Wang, Lusheng ; Xue, Guoliang. / Approximations for Steiner Trees with Minimum Number of Steiner Points. In: Journal of Global Optimization. 2000 ; Vol. 18, No. 1. pp. 17-33.
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