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arXiv · 1509.07214

Computing the Geodesic Centers of a Polygonal Domain

Sang Won Bae·Matias Korman·Yoshio Okamoto
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Abstract

We present an algorithm that computes the geodesic center of a given polygonal domain. The running time of our algorithm is $O(n^{12+\epsilon})$ for any $\epsilon>0$, 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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Sang Won Bae, Matias Korman, Yoshio Okamoto. 2015-09-24. Computing the Geodesic Centers of a Polygonal Domain. https://arxiv.org/abs/1509.07214

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