### Abstract

Given an edge-weighted undirected graph G = (V, E, c, w), where each edge e E has a non-negative cost c(e) and a non-negative weight w(e), a set S V of terminals and a positive constant D_{0}, we seek a minimum cost Steiner tree in which all terminals appear as leaves and the tree diameter is bounded by D_{0}. Here the tree diameter is the maximum weight of the paths connecting two different leaves in the tree. Such a problem is called the minimum cost diameter-constrained Steiner tree problem. The problem is NP-hard even when the topology of the Steiner tree is fixed. In present paper we focus on this fixed topology restricted version and present a fully polynomial time approximation scheme for computing a minimum cost diameter-constrained Steiner tree.

Original language | English (US) |
---|---|

Pages (from-to) | 491-502 |

Number of pages | 12 |

Journal | Discrete Mathematics, Algorithms and Applications |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2011 |

### Fingerprint

### Keywords

- Diameter-constrained Steiner tree
- fixed topology
- fully polynomial time approximation scheme

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*Discrete Mathematics, Algorithms and Applications*,

*3*(4), 491-502. https://doi.org/10.1142/S179383091100136X

**Diameter-constrained steiner trees.** / Ding, W. E.I.; Lin, Guohui; Xue, Guoliang.

Research output: Contribution to journal › Article

*Discrete Mathematics, Algorithms and Applications*, vol. 3, no. 4, pp. 491-502. https://doi.org/10.1142/S179383091100136X

}

TY - JOUR

T1 - Diameter-constrained steiner trees

AU - Ding, W. E.I.

AU - Lin, Guohui

AU - Xue, Guoliang

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Given an edge-weighted undirected graph G = (V, E, c, w), where each edge e E has a non-negative cost c(e) and a non-negative weight w(e), a set S V of terminals and a positive constant D0, we seek a minimum cost Steiner tree in which all terminals appear as leaves and the tree diameter is bounded by D0. Here the tree diameter is the maximum weight of the paths connecting two different leaves in the tree. Such a problem is called the minimum cost diameter-constrained Steiner tree problem. The problem is NP-hard even when the topology of the Steiner tree is fixed. In present paper we focus on this fixed topology restricted version and present a fully polynomial time approximation scheme for computing a minimum cost diameter-constrained Steiner tree.

AB - Given an edge-weighted undirected graph G = (V, E, c, w), where each edge e E has a non-negative cost c(e) and a non-negative weight w(e), a set S V of terminals and a positive constant D0, we seek a minimum cost Steiner tree in which all terminals appear as leaves and the tree diameter is bounded by D0. Here the tree diameter is the maximum weight of the paths connecting two different leaves in the tree. Such a problem is called the minimum cost diameter-constrained Steiner tree problem. The problem is NP-hard even when the topology of the Steiner tree is fixed. In present paper we focus on this fixed topology restricted version and present a fully polynomial time approximation scheme for computing a minimum cost diameter-constrained Steiner tree.

KW - Diameter-constrained Steiner tree

KW - fixed topology

KW - fully polynomial time approximation scheme

UR - http://www.scopus.com/inward/record.url?scp=84864999927&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864999927&partnerID=8YFLogxK

U2 - 10.1142/S179383091100136X

DO - 10.1142/S179383091100136X

M3 - Article

VL - 3

SP - 491

EP - 502

JO - Discrete Mathematics, Algorithms and Applications

JF - Discrete Mathematics, Algorithms and Applications

SN - 1793-8309

IS - 4

ER -