### Abstract

In this paper, we study the Steiner tree problem in the λ4-geometry plane in which any line, half line or line segment must go in an orientation of iπ/4 with the positive x-axis, 0 ≤ i ≤ 7, and the distance between two points is the length of the shortest polygonal path connecting them. We show that for any set of n terminal points, there exists a Steiner minimal tree interconnecting these terminal points such that all Steiner points are in G _{⌊2n/3⌋-1}, the (⌊2n/3⌋r - 1) ^{st}-generation grid points formed by the n terminal points. Our result improves previous known result which guarantees that for any set of n terminal points, there is a Steiner minimal tree in which all Steiner points are in G_{n - 2}.

Original language | English (US) |
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Title of host publication | Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings |

Publisher | Springer Verlag |

Pages | 327-337 |

Number of pages | 11 |

ISBN (Print) | 3540653856, 9783540653851 |

DOIs | |

State | Published - 1998 |

Externally published | Yes |

Event | 9th Annual International Symposium on Algorithms and Computation, ISAAC'98 - Taejon, Korea, Republic of Duration: Dec 14 1998 → Dec 16 1998 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1533 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 9th Annual International Symposium on Algorithms and Computation, ISAAC'98 |
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Country | Korea, Republic of |

City | Taejon |

Period | 12/14/98 → 12/16/98 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

_{4}-geometry plane. In

*Algorithms and Computation - 9th International Symposium, ISAAC'98, Proceedings*(pp. 327-337). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1533 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-49381-6_35