### Abstract

We show that, in any given uniform orientation metric plane, the shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations. When the given topology is restricted to a Steiner topology, our result implies that the Steiner minimum tree under a given Steiner topology can be computed in polynomial time in any given uniform orientation metric with λ legal orientations for any fixed integer λ ≥ 2. This settles an open problem posed in a recent paper.

Original language | English (US) |
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Pages (from-to) | 1117-1120 |

Number of pages | 4 |

Journal | IEEE Transactions on Computers |

Volume | 51 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1 2002 |

### Keywords

- Linear programming
- Shortest network under a fixed topology
- Steiner trees
- Uniform orientation metric plane

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computational Theory and Mathematics

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## Cite this

Xue, G., & Thulasiraman, K. (2002). Computing the shortest network under a fixed topology.

*IEEE Transactions on Computers*,*51*(9), 1117-1120. https://doi.org/10.1109/TC.2002.1032631