Approximations for Steiner Trees with Minimum Number of Steiner Points

  • Authors:

  • Donghui Chen;Ding-Zhu Du;Xiao-Dong Hu;Guo-Hui Lin;Lusheng Wang;Guoliang Xue

  • Affiliations:

  • Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN 55455, USA (E-mail: dzd@cs.umn.edu );Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN 55455, USA (E-mail: dzd@cs.umn.edu ) Department of Computer Science, City University of Ho ...;Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong, China Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China;Department of Computer Science, The University of Vermont, Burlington, VT 05405, USA;Department of Computer Science, City University of Hong Kong, Kowloon Tong, Hong Kong, China;Department of Computer Science, The University of Vermont, Burlington, VT 05405, USA

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2000

Quantified Score

Hi-index 0.00

Visualization

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 approxi-mation scheme under certain conditions.