## Abstract

We consider the problem of constructing a shortest Euclidean 2-connected Steiner network in the plane (SMN) for a set of n terminals. This problem has natural applications in the design of survivable communication networks.

In [P. Winter, M. Zachariasen, Two-connected Steiner networks: Structural properties, OR Letters 33 (2005) 395–402] we proved that all cycles in SMNs with Steiner points must have pairs of consecutive terminals of degree 2. We use this result and the notion of reduced block-bridge trees suggested by Luebke [E.L. Luebke, k-connected Steiner network problems, PhD thesis, University of North Carolina, USA, 2002] to show that no full Steiner tree in a SMN spans more than (n/3)+1 terminals.

In [P. Winter, M. Zachariasen, Two-connected Steiner networks: Structural properties, OR Letters 33 (2005) 395–402] we proved that all cycles in SMNs with Steiner points must have pairs of consecutive terminals of degree 2. We use this result and the notion of reduced block-bridge trees suggested by Luebke [E.L. Luebke, k-connected Steiner network problems, PhD thesis, University of North Carolina, USA, 2002] to show that no full Steiner tree in a SMN spans more than (n/3)+1 terminals.

Original language | English |
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Pages (from-to) | 159-163 |

Number of pages | 5 |

Journal | Information Processing Letters |

Volume | 104 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2007 |

## Keywords

- computational geometry
- interconnection networks
- 2-connected Steiner networks