@inproceedings{ffb1f1bad9664dbbb10cd4bd4c742246,

title = "A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon",

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.",

keywords = "1-center problem, Facility location, Geodesic distance, Simple polygons",

author = "Ahn, {Hee Kap} and Luis Barba and Prosenjit Bose and {De Carufel}, {Jean Lou} and Matias Korman and Eunjin Oh",

year = "2015",

month = jun,

day = "1",

doi = "10.4230/LIPIcs.SOCG.2015.209",

language = "English",

series = "Leibniz International Proceedings in Informatics, LIPIcs",

publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",

pages = "209--223",

editor = "Janos Pach and Janos Pach and Lars Arge",

booktitle = "31st International Symposium on Computational Geometry, SoCG 2015",

note = "31st International Symposium on Computational Geometry, SoCG 2015 ; Conference date: 22-06-2015 Through 25-06-2015",

}