### Abstract

This paper is concerned with a simple, rather intuitive preprocessing step that is likely to improve the average-case performance of any convex hull algorithm. For n points randomly distributed in the unit square, we show that a simple linear pass through the points can eliminate all but O(√n) of the points by showing that a simple superset of the remaining points has size c√n + o(√n). We give a full implementation of the method, which should be useful in any practical application for finding convex hulls. Most of the paper is concerned with an analysis of the number of points eliminated by the procedure, including derivation of an exact expression for c. Extensions to higher dimensions are also considered.

Original language | English (US) |
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Title of host publication | Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988 |

Publisher | Association for Computing Machinery, Inc |

Pages | 153-163 |

Number of pages | 11 |

ISBN (Electronic) | 0897912705, 9780897912709 |

DOIs | |

State | Published - Jan 6 1988 |

Event | 4th Annual Symposium on Computational Geometry, SCG 1988 - Urbana-Champaign, United States Duration: Jun 6 1988 → Jun 8 1988 |

### Publication series

Name | Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988 |
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### Other

Other | 4th Annual Symposium on Computational Geometry, SCG 1988 |
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Country | United States |

City | Urbana-Champaign |

Period | 6/6/88 → 6/8/88 |

### All Science Journal Classification (ASJC) codes

- Geometry and Topology

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## Cite this

*Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988*(pp. 153-163). (Proceedings of the 4th Annual Symposium on Computational Geometry, SCG 1988). Association for Computing Machinery, Inc. https://doi.org/10.1145/73393.73409