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

doi:10.1023/A:1008384012064

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 journal › Article › peer-review

123 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 language	English (US)
Pages (from-to)	17-33
Number of pages	17
Journal	Journal of Global Optimization
Volume	18
Issue number	1
DOIs	https://doi.org/10.1023/A:1008384012064
State	Published - Sep 2000
Externally published	Yes

Keywords

Approximation algorithms
Steiner trees
VLSI design
WDM optical networks

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics
Business, Management and Accounting (miscellaneous)
Computer Science Applications
Management Science and Operations Research

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10.1023/A:1008384012064

Cite this

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title = "Approximations for Steiner Trees with Minimum Number of Steiner Points",

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.",

keywords = "Approximation algorithms, Steiner trees, VLSI design, WDM optical networks",

author = "Donghui Chen and Du, {Ding Zhu} and Hu, {Xiao Dong} and Lin, {Guo Hui} and Lusheng Wang and Guoliang Xue",

note = "Funding Information: ∗Corresponding author. E-mail addresses: dchen@cs.umn.edu (D. Chen), dzd@cs.umn.edu, dzd@cs.cityu.edu.hk (D.-Z. Du), xdhu@cs.cityu.edu.hk (X.-D. Hu), ghlin@cs.uvm.edu (G.-H. Lin), wang@cs.cityu.edu.hk (L. Wang), and xue@cs.uvm.edu (G. Xue). 1Support in part by the National Science Foundation under Grant CCR-9530306. 2Support in part by National Natural Science Foundation of China under Grant 19331050. 3Supported in part by the Army Research OCce Grant DAAH04-96-10233 and by the National Science Foundation Grants ASC-9409285 and OSR-9350540.",

year = "2000",

month = sep,

doi = "10.1023/A:1008384012064",

language = "English (US)",

volume = "18",

pages = "17--33",

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AU - Chen, Donghui

AU - Du, Ding Zhu

AU - Hu, Xiao Dong

AU - Lin, Guo Hui

AU - Wang, Lusheng

AU - Xue, Guoliang

N1 - Funding Information: ∗Corresponding author. E-mail addresses: dchen@cs.umn.edu (D. Chen), dzd@cs.umn.edu, dzd@cs.cityu.edu.hk (D.-Z. Du), xdhu@cs.cityu.edu.hk (X.-D. Hu), ghlin@cs.uvm.edu (G.-H. Lin), wang@cs.cityu.edu.hk (L. Wang), and xue@cs.uvm.edu (G. Xue). 1Support in part by the National Science Foundation under Grant CCR-9530306. 2Support in part by National Natural Science Foundation of China under Grant 19331050. 3Supported in part by the Army Research OCce Grant DAAH04-96-10233 and by the National Science Foundation Grants ASC-9409285 and OSR-9350540.

PY - 2000/9

Y1 - 2000/9

N2 - 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.

AB - 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.

KW - Approximation algorithms

KW - Steiner trees

KW - VLSI design

KW - WDM optical networks

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Approximations for Steiner Trees with Minimum Number of Steiner Points

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