### 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) | 83-99 |

Number of pages | 17 |

Journal | Theoretical Computer Science |

Volume | 262 |

Issue number | 1-2 |

DOIs | |

State | Published - 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computational Theory and Mathematics

### Cite this

*Theoretical Computer Science*,

*262*(1-2), 83-99. https://doi.org/10.1016/S0304-3975(00)00182-1

**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.

Research output: Contribution to journal › Article

*Theoretical Computer Science*, vol. 262, no. 1-2, pp. 83-99. https://doi.org/10.1016/S0304-3975(00)00182-1

}

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

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

UR - http://www.scopus.com/inward/record.url?scp=0034911862&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034911862&partnerID=8YFLogxK

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

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

M3 - Article

AN - SCOPUS:0034911862

VL - 262

SP - 83

EP - 99

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1-2

ER -