### Abstract

Let P be a closed simple polygon with n vertices. For any two points in P, the geodesic distance between them is the length of the shortest path that connects them among all paths contained in P. The geodesic center of P is the unique point in P that minimizes the largest geodesic distance to all other points of P. In 1989, Pollack, Sharir and Rote [Disc. & Comput. Geom. 89] showed an O(n log n)-time algorithm that computes the geodesic center of P. Since then, a longstanding question has been whether this running time can be improved (explicitly posed by Mitchell [Handbook of Computational Geometry, 2000]). In this paper we affirmatively answer this question and present a linear time algorithm to solve this problem.

Original language | English |
---|---|

Title of host publication | 31st International Symposium on Computational Geometry, SoCG 2015 |

Editors | Janos Pach, Janos Pach, Lars Arge |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Pages | 209-223 |

Number of pages | 15 |

ISBN (Electronic) | 9783939897835 |

DOIs | |

Publication status | Published - 2015 Jun 1 |

Externally published | Yes |

Event | 31st International Symposium on Computational Geometry, SoCG 2015 - Eindhoven, Netherlands Duration: 2015 Jun 22 → 2015 Jun 25 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
---|---|

Volume | 34 |

ISSN (Print) | 1868-8969 |

### Other

Other | 31st International Symposium on Computational Geometry, SoCG 2015 |
---|---|

Country | Netherlands |

City | Eindhoven |

Period | 15/6/22 → 15/6/25 |

### Keywords

- 1-center problem
- Facility location
- Geodesic distance
- Simple polygons

### ASJC Scopus subject areas

- Software

## Fingerprint Dive into the research topics of 'A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon'. Together they form a unique fingerprint.

## Cite this

*31st International Symposium on Computational Geometry, SoCG 2015*(pp. 209-223). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 34). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SOCG.2015.209