### Abstract

We present a near-quadratic time algorithm that computes a point inside a simple polygon P having approximately the largest visibility polygon inside P, and near-linear time algorithm for finding the point that will have approximately the largest Voronoi region when added to an n-point set. We apply the same technique to find the translation that approximately maximizes the area of intersection of two polygonal regions in near-quadratic time.

Original language | English (US) |
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Pages | 1091-1100 |

Number of pages | 10 |

State | Published - Apr 15 2004 |

Event | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms - New Orleans, LA., United States Duration: Jan 11 2004 → Jan 13 2004 |

### Other

Other | Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms |
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Country | United States |

City | New Orleans, LA. |

Period | 1/11/04 → 1/13/04 |

### ASJC Scopus subject areas

- Software
- Mathematics(all)

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## Cite this

Cheong, O., Efrat, A., & Har-Peled, S. (2004).

*On Finding a Guard that Sees Most and a Shop that Sells Most*. 1091-1100. Paper presented at Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA., United States.