Elsevier

Computational Geometry

Volume 77, March 2019, Pages 3-9
Computational Geometry

Computing the geodesic centers of a polygonal domain

https://doi.org/10.1016/j.comgeo.2015.10.009Get rights and content
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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(n12+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(nlogn)-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.

Keywords

Polygonal domain
Shortest path
Geodesic center
Exact algorithm

Cited by (0)

A preliminary version of this paper was presented at the 26th Canadian Conference on Computational Geometry (CCCG'14) [4]. Work by S.W. Bae was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2013R1A1A1A05006927). Work by M. Korman was partially supported by the ELC project (MEXT KAKENHI No. 24106008). Work by Y. Okamoto was partially supported by Grant-in-Aid for Scientific Research from Ministry of Education, Science and Culture, Japan and Japan Society for the Promotion of Science, and the ELC project (Grant-in-Aid for Scientific Research on Innovative Areas, MEXT Japan).