### Abstract

Given an edge-weighted undirected graph G = (V,E,c,w) where each edge e ∈ E has a cost c(e) ≥ 0 and another weight w(e) ≥ 0, a set S ⊆ V of terminals and a given constant 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 C _{0}. The diameter of tree refers to the maximum weight of the paths 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 specific characteristic.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 37-48 |

Number of pages | 12 |

Volume | 7402 LNCS |

DOIs | |

State | Published - 2012 |

Event | 6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012 - Banff, AB, Canada Duration: Aug 5 2012 → Aug 9 2012 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 7402 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012 |
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Country | Canada |

City | Banff, AB |

Period | 8/5/12 → 8/9/12 |

### Fingerprint

### Keywords

- cost-constrained Steiner tree
- fixed topology
- Minimum diameter
- weakly fully polynomial time approximation scheme

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 7402 LNCS, pp. 37-48). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7402 LNCS). https://doi.org/10.1007/978-3-642-31770-5_4

**On the minimum diameter cost-constrained steiner tree problem.** / Ding, Wei; Xue, Guoliang.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 7402 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7402 LNCS, pp. 37-48, 6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012, Banff, AB, Canada, 8/5/12. https://doi.org/10.1007/978-3-642-31770-5_4

}

TY - GEN

T1 - On the minimum diameter cost-constrained steiner tree problem

AU - Ding, Wei

AU - Xue, Guoliang

PY - 2012

Y1 - 2012

N2 - Given an edge-weighted undirected graph G = (V,E,c,w) where each edge e ∈ E has a cost c(e) ≥ 0 and another weight w(e) ≥ 0, a set S ⊆ V of terminals and a given constant 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 C 0. The diameter of tree refers to the maximum weight of the paths 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 specific characteristic.

AB - Given an edge-weighted undirected graph G = (V,E,c,w) where each edge e ∈ E has a cost c(e) ≥ 0 and another weight w(e) ≥ 0, a set S ⊆ V of terminals and a given constant 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 C 0. The diameter of tree refers to the maximum weight of the paths 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 specific characteristic.

KW - cost-constrained Steiner tree

KW - fixed topology

KW - Minimum diameter

KW - weakly fully polynomial time approximation scheme

UR - http://www.scopus.com/inward/record.url?scp=84864973156&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864973156&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31770-5_4

DO - 10.1007/978-3-642-31770-5_4

M3 - Conference contribution

AN - SCOPUS:84864973156

SN - 9783642317699

VL - 7402 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 37

EP - 48

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -