### 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) |
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Pages (from-to) | 491-502 |

Number of pages | 12 |

Journal | Discrete Mathematics, Algorithms and Applications |

Volume | 3 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 2011 |

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### 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