### Abstract

The link center of a simple polygon P is the set of points x inside P at which the maximal link-distance from x to any other point in P is minimized. Here the link distance between two points x, y inside P is defined to be the smallest number of straight edges in a polygonal path inside P connecting x to y. We prove several geometric properties of the link center and present an algorithm that calculates this set in time O(n^{2}), where n is the number of sides of P. We also give an O(n log n) algorithm for finding an approximate link center, that is, a point x such that the maximal link distance from x to any point in P is at most one more than the value attained from the true link center.

Original language | English (US) |
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Pages (from-to) | 281-293 |

Number of pages | 13 |

Journal | Discrete and Computational Geometry |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1988 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

*Discrete and Computational Geometry*,

*3*(1), 281-293. https://doi.org/10.1007/BF02187913

**Computing the link center of a simple polygon.** / Lenhart, W.; Pollack, R.; Sack, J.; Seidel, R.; Sharir, M.; Suri, S.; Toussaint, Godfried; Whitesides, S.; Yap, Chee.

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 3, no. 1, pp. 281-293. https://doi.org/10.1007/BF02187913

}

TY - JOUR

T1 - Computing the link center of a simple polygon

AU - Lenhart, W.

AU - Pollack, R.

AU - Sack, J.

AU - Seidel, R.

AU - Sharir, M.

AU - Suri, S.

AU - Toussaint, Godfried

AU - Whitesides, S.

AU - Yap, Chee

PY - 1988/12

Y1 - 1988/12

N2 - The link center of a simple polygon P is the set of points x inside P at which the maximal link-distance from x to any other point in P is minimized. Here the link distance between two points x, y inside P is defined to be the smallest number of straight edges in a polygonal path inside P connecting x to y. We prove several geometric properties of the link center and present an algorithm that calculates this set in time O(n2), where n is the number of sides of P. We also give an O(n log n) algorithm for finding an approximate link center, that is, a point x such that the maximal link distance from x to any point in P is at most one more than the value attained from the true link center.

AB - The link center of a simple polygon P is the set of points x inside P at which the maximal link-distance from x to any other point in P is minimized. Here the link distance between two points x, y inside P is defined to be the smallest number of straight edges in a polygonal path inside P connecting x to y. We prove several geometric properties of the link center and present an algorithm that calculates this set in time O(n2), where n is the number of sides of P. We also give an O(n log n) algorithm for finding an approximate link center, that is, a point x such that the maximal link distance from x to any point in P is at most one more than the value attained from the true link center.

UR - http://www.scopus.com/inward/record.url?scp=0041111213&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041111213&partnerID=8YFLogxK

U2 - 10.1007/BF02187913

DO - 10.1007/BF02187913

M3 - Article

AN - SCOPUS:0041111213

VL - 3

SP - 281

EP - 293

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -