### Abstract

We give a dynamic data structure that can maintain an e-coreset of n points, with respect to the extent measure, in O(log n) time for any constant ε > 0 and any constant dimension. The previous method by Agarwal, Har-Peled, and Varadarajan requires polylogarithmic update time. For points with integer coordinates bounded by U, we alternatively get 0(log log U) time. Numerous applications follow, for example, on dynamically approximating the width, smallest enclosing cylinder, minimum bounding box, or minimum-width annulus. We can also use the same approach to maintain approximate fc-centers in 0(min{log n, log log U}) randomized amortized time for any constant k and any constant dimension. For the smallest enclosing cylinder problem, we also show that a constant-factor approximation can be maintained in O(l) randomized amortized time on the word RAM.

Original language | English (US) |
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Title of host publication | Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08 |

Pages | 1-9 |

Number of pages | 9 |

DOIs | |

State | Published - Dec 12 2008 |

Externally published | Yes |

Event | 24th Annual Symposium on Computational Geometry, SCG'08 - College Park, MD, United States Duration: Jun 9 2008 → Jun 11 2008 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Other

Other | 24th Annual Symposium on Computational Geometry, SCG'08 |
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Country | United States |

City | College Park, MD |

Period | 6/9/08 → 6/11/08 |

### Keywords

- Approximation algorithms
- Dynamic data structures
- Geometric optimization
- Randomization
- Word RAM

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Mathematics

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## Cite this

*Proceedings of the 24th Annual Symposium on Computational Geometry 2008, SCG'08*(pp. 1-9). (Proceedings of the Annual Symposium on Computational Geometry). https://doi.org/10.1145/1377676.1377680