### 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 |

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### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Applied Mathematics
- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Applied Mathematics*,

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

**Computing external farthest neighbors for a simple polygon.** / Agarwal, Pankaj K.; Aggarwal, Alok; Aronov, Boris; Kosaraju, S. Rao; Schieber, Baruch; Suri, Subhash.

Research output: Contribution to journal › Article

*Discrete Applied Mathematics*, vol. 31, no. 2, pp. 97-111. https://doi.org/10.1016/0166-218X(91)90063-3

}

TY - JOUR

T1 - Computing external farthest neighbors for a simple polygon

AU - Agarwal, Pankaj K.

AU - Aggarwal, Alok

AU - Aronov, Boris

AU - Kosaraju, S. Rao

AU - Schieber, Baruch

AU - Suri, Subhash

PY - 1991/4/15

Y1 - 1991/4/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=4043153839&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4043153839&partnerID=8YFLogxK

U2 - 10.1016/0166-218X(91)90063-3

DO - 10.1016/0166-218X(91)90063-3

M3 - Article

AN - SCOPUS:4043153839

VL - 31

SP - 97

EP - 111

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 2

ER -