### 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) |
---|---|

Pages (from-to) | 1117-1120 |

Number of pages | 4 |

Journal | IEEE Transactions on Computers |

Volume | 51 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2002 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture

### Cite this

*IEEE Transactions on Computers*,

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

**Computing the shortest network under a fixed topology.** / Xue, Guoliang; Thulasiraman, K.

Research output: Contribution to journal › Article

*IEEE Transactions on Computers*, vol. 51, no. 9, pp. 1117-1120. https://doi.org/10.1109/TC.2002.1032631

}

TY - JOUR

T1 - Computing the shortest network under a fixed topology

AU - Xue, Guoliang

AU - Thulasiraman, K.

PY - 2002/9

Y1 - 2002/9

N2 - 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.

AB - 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.

KW - Linear programming

KW - Shortest network under a fixed topology

KW - Steiner trees

KW - Uniform orientation metric plane

UR - http://www.scopus.com/inward/record.url?scp=0036709609&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036709609&partnerID=8YFLogxK

U2 - 10.1109/TC.2002.1032631

DO - 10.1109/TC.2002.1032631

M3 - Article

AN - SCOPUS:0036709609

VL - 51

SP - 1117

EP - 1120

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

SN - 0018-9340

IS - 9

ER -