### 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 |

State | Published - Sep 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Management Science and Operations Research
- Global and Planetary Change
- Applied Mathematics
- Control and Optimization

### Cite this

*Journal of Global Optimization*,

*18*(1), 17-33.

**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

*Journal of Global Optimization*, vol. 18, no. 1, pp. 17-33.

}

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 - 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

UR - http://www.scopus.com/inward/record.url?scp=0006687948&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0006687948&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0006687948

VL - 18

SP - 17

EP - 33

JO - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 1

ER -