### Abstract

For a set S contained in a metric space, a Steiner tree of S is a tree that connects the points in S. Finding a minimum cost Steiner tree is an NP-hard problem in euclidean and rectilinear metrics as well as in graphs. We give an approximation algorithm and show that the worst-case ratio of the cost of our solutions to the optimal cost is better than previously known ratios in graphs, and in rectilinear metric on the plane. Our method offers a tradeoff between the running time and the ratio; on one hand it always allows to improve the ratio, on the other it allows to obtain previously known ratios with much greater efficiency. We use properties of optimal rectilinear Steiner trees to obtain significantly better ratio and running time in rectilinear metric.

Original language | English (US) |
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Title of host publication | Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 |

Publisher | Association for Computing Machinery |

Pages | 325-334 |

Number of pages | 10 |

ISBN (Electronic) | 089791466X |

State | Published - Sep 1 1992 |

Event | 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 - Orlando, United States Duration: Jan 27 1992 → Jan 29 1992 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | Part F129721 |

### Other

Other | 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 |
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Country | United States |

City | Orlando |

Period | 1/27/92 → 1/29/92 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

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## Cite this

*Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992*(pp. 325-334). (Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms; Vol. Part F129721). Association for Computing Machinery.