### 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 & Computational Geometry |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1988 |

### ASJC Scopus subject areas

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

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## Cite this

*Discrete & Computational Geometry*,

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