TY - JOUR

T1 - Approximations for Steiner trees with minimum number of Steiner points

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 - 2001

Y1 - 2001

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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U2 - 10.1016/S0304-3975(00)00182-1

DO - 10.1016/S0304-3975(00)00182-1

M3 - Article

AN - SCOPUS:0034911862

SN - 0304-3975

VL - 262

SP - 83

EP - 99

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1-2

ER -