Computing the Geodesic Centers of a Polygonal Domain

2015/09/24 by Bae, Sang Won, Korman, Matias, Okamoto, Yoshio
#Computational Geometry (cs.CG) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.1509.07214

Abstract

We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is O(n^12+ε) for any ε>0, where n is the number of corners of the input polygonal domain. Prior to our work, only the very special case where a simple polygon is given as input has been intensively studied in the 1980s, and an O(n log n)-time algorithm is known by Pollack et al. Our algorithm is the first one that can handle general polygonal domains having one or more polygonal holes.

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