@article{36dd4ccc8e3b45508618eec4a05f9e6b,

title = "Computing the geodesic centers of a polygonal domain",

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 = "Exact algorithm, Geodesic center, Polygonal domain, Shortest path",

author = "Bae, {Sang Won} and Matias Korman and Yoshio Okamoto",

note = "Funding Information: A preliminary version of this paper was presented at the 26th Canadian Conference on Computational Geometry (CCCG{\textquoteright}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). Publisher Copyright: {\textcopyright} 2015 Elsevier B.V.",

year = "2019",

month = mar,

doi = "10.1016/j.comgeo.2015.10.009",

language = "English",

volume = "77",

pages = "3--9",

journal = "Computational Geometry: Theory and Applications",

issn = "0925-7721",

publisher = "Elsevier",

}