### 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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Title of host publication | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |

Pages | 1091-1100 |

Number of pages | 10 |

Volume | 15 |

State | Published - 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 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Discrete Mathematics and Combinatorics
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms*(Vol. 15, pp. 1091-1100)

**On Finding a Guard that Sees Most and a Shop that Sells Most.** / Cheong, Otfried; Efrat, Alon; Har-Peled, Sariel.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms.*vol. 15, pp. 1091-1100, Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA., United States, 1/11/04.

}

TY - GEN

T1 - On Finding a Guard that Sees Most and a Shop that Sells Most

AU - Cheong, Otfried

AU - Efrat, Alon

AU - Har-Peled, Sariel

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=1842538784&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1842538784&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:1842538784

VL - 15

SP - 1091

EP - 1100

BT - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

ER -