### Abstract

Given a set of n hyperplanes h_{l},.... h_{n} ε R^{d} the hyperplane depth of a point P ε R^{d} is the minimum number of hyperplanes that a ray from P can meet. The hyperplane depth of the arrangement is the maximal depth of points P not in any h_{i}. We give an optimal O(n log n) deterministic algorithm to compute the hyperplane depth of an arrangement in dimension d = 2.

Original language | English (US) |
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Pages | 54-59 |

Number of pages | 6 |

State | Published - Jan 1 2000 |

Event | 11th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, USA Duration: Jan 9 2000 → Jan 11 2000 |

### Other

Other | 11th Annual ACM-SIAM Symposium on Discrete Algorithms |
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City | San Francisco, CA, USA |

Period | 1/9/00 → 1/11/00 |

### All Science Journal Classification (ASJC) codes

- Software
- Mathematics(all)

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## Cite this

Langerman, S., & Steiger, W. (2000).

*Optimal algorithm for hyperplane depth in the plane*. 54-59. Paper presented at 11th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, USA, .