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A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon Ahn, Hee Kap Barba, Luis Bose, Prosenjit De Carufel, Jean-Lou Korman, Matias Oh, Eunjin Geodesic distance facility location 1-center problem simple polygons 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Hee Kap Ahn and Luis Barba and Prosenjit Bose and Jean-Lou De Carufel and Matias Korman and Eunjin Oh 2015 Is Part Of LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SOCG.2015.209 urn:nbn:de:0030-drops-51448 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.209 eng https://creativecommons.org/licenses/by/3.0/legalcode