### Abstract

Let P be (the boundary of) a simple polygon with n vertices. For a vertex p of P, let φ{symbol}(p) be the set of points on P that are farthest from p, where the distance between two points is the length of the (Euclidean) shortest path that connects them without intersecting the interior of P. In this paper, we present an O(n log n) algorithm to compute a member of φ{symbol}(p) for every vertex p of P. As a corollary, the external diameter of P can also be computed in the same time.

Original language | English (US) |
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Pages (from-to) | 97-111 |

Number of pages | 15 |

Journal | Discrete Applied Mathematics |

Volume | 31 |

Issue number | 2 |

DOIs | |

State | Published - Apr 15 1991 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Agarwal, P. K., Aggarwal, A., Aronov, B., Kosaraju, S. R., Schieber, B., & Suri, S. (1991). Computing external farthest neighbors for a simple polygon.

*Discrete Applied Mathematics*,*31*(2), 97-111. https://doi.org/10.1016/0166-218X(91)90063-3