### Abstract

Given an edge-weighted undirected graph G=(V,E,c,w) where each edge eεE has a cost c(e)≥0 and another weight w(e)≥0, a set S⊂ V of terminals and a given constant \mathrm{C}-0≥0, the aim is to find a minimum diameter Steiner tree whose all terminals appear as leaves and the cost of tree is bounded by \mathrm{C}-0. The diameter of a tree refers to the maximum weight of the path connecting two different leaves in the tree. This problem is called the minimum diameter cost-constrained Steiner tree problem, which is NP-hard even when the topology of the Steiner tree is fixed. In this paper, we deal with the fixed-topology restricted version. We prove the restricted version to be polynomially solvable when the topology is not part of the input and propose a weakly fully polynomial time approximation scheme (weakly FPTAS) when the topology is part of the input, which can find a (1+ε) -approximation of the restricted version problem for any ε >0 with a specific characteristic.

Original language | English (US) |
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Pages (from-to) | 32-48 |

Number of pages | 17 |

Journal | Journal of Combinatorial Optimization |

Volume | 27 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2014 |

### ASJC Scopus subject areas

- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics

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## Cite this

*Journal of Combinatorial Optimization*,

*27*(1), 32-48. https://doi.org/10.1007/s10878-013-9611-2