A Linear-Time Algorithm for the Geodesic Center of a Simple Polygon
نویسندگان
چکیده
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 logn)-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. 1998 ACM Subject Classification I.3.5 Computational Geometry and Object Modeling
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