### Abstract

We show that, using the L_{∞} metric, the minimum Hausdorff distance under translation between two point sets of cardinality n in ddimensional space can be computed in time O(n^{(4d-2)/3}1og^{2} n) for d > 3. Thus we improve the previous time bound of O(n^{2d-2} log^{2} n) due to Chew and Kedem. For d = 3 we obtain a better result of O(n^{3} log^{2} n) time by exploiting the fact that the union of n axis-parallel unit cubes can be decomposed into O(n) disjoint axls-parallel boxes. We prove that the number of different translations that azhieve the minimum Hausdorff distance in dspace is Θ (n^{[3d/2]}). Furthermore, we present an algorithm which computes the minimum Hausdorff distance under the L_{2} metric in d-space in time O(n^{[3d/2]+l} log^{3} n).

Original language | English (US) |
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Title of host publication | Algorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings |

Editors | Paul Spirakis |

Publisher | Springer-Verlag |

Pages | 264-279 |

Number of pages | 16 |

ISBN (Print) | 3540603131, 9783540603139 |

State | Published - Jan 1 1995 |

Externally published | Yes |

Event | 3rd Annual European Symposium on Algorithms, ESA 1995 - Corfu, Greece Duration: Sep 25 1995 → Sep 27 1995 |

### 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 | 979 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Annual European Symposium on Algorithms, ESA 1995 |
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Country | Greece |

City | Corfu |

Period | 9/25/95 → 9/27/95 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Algorithms - ESA 1995 - 3rd Annual European Symposium, Proceedings*(pp. 264-279). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 979). Springer-Verlag.