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

114 Scopus citations

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
DOIs
StatePublished - Sep 2000
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research
  • Control and Optimization
  • Applied Mathematics

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