https://scholars.lib.ntu.edu.tw/handle/123456789/624638
標題: | A nearly optimal algorithm for the geodesic voronoi diagram of points in a simple polygon | 作者: | CHIH-HUNG LIU | 關鍵字: | Geodesic distance; Simple polygons; Voronoi diagrams | 公開日期: | 2018 | 卷: | 99 | 起(迄)頁: | 581-5814 | 來源出版物: | Leibniz International Proceedings in Informatics, LIPIcs | 摘要: | The geodesic Voronoi diagram ofm point sites inside a simple polygon of n vertices is a subdivision of the polygon into m cells, one to each site, such that all points in a cell share the same nearest site under the geodesic distance. The best known lower bound for the construction time is Ω(n + mlogm), and a matching upper bound is a long-standing open question. The state-of-the-art construction algorithms achieve O((n + m) log(n + m)) and O(n + mlogmlog2 n) time, which are optimal for m = Ω(n) and m = O(n/log3 n), respectively. In this paper, we give a construction algorithm with O(n + m(logm + log2 n)) time, and it is nearly optimal in the sense that if a single Voronoi vertex can be computed in O(logn) time, then the construction time will become the optimal O(n + m log m). In other words, we reduce the problem of constructing the diagram in the optimal time to the problem of computing a single Voronoi vertex in O(logn) time. © Chih-Hung Liu; licensed under Creative Commons License CC-BY 34th Symposium on Computational Geometry (SoCG 2018). |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85048980271&doi=10.4230%2fLIPIcs.SoCG.2018.58&partnerID=40&md5=a43741a72faaa90acf6022ec11f43cca https://scholars.lib.ntu.edu.tw/handle/123456789/624638 |
ISSN: | 18688969 | DOI: | 10.4230/LIPIcs.SoCG.2018.58 | SDG/關鍵字: | Geodesy; Graphic methods; Construction algorithms; Construction time; Geodesic distances; Geodesic voronoi diagram; Optimal algorithm; Simple polygon; State of the art; Voronoi diagrams; Computational geometry |
顯示於: | 電機工程學系 |
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