https://scholars.lib.ntu.edu.tw/handle/123456789/624644
標題: | A randomized divide and conquer algorithm for higher-order abstract Voronoi diagrams | 作者: | Bohler C Liu C.-H Papadopoulou E Zavershynskyi M. CHIH-HUNG LIU |
關鍵字: | Abstract Voronoi diagram; Divide and conquer; Geometric randomized algorithm; Higher-order Voronoi diagram; k nearest neighbors | 公開日期: | 2016 | 卷: | 59 | 起(迄)頁: | 26-38 | 來源出版物: | Computational Geometry: Theory and Applications | 摘要: | Given a set of n sites in the plane, their order-k Voronoi diagram partitions the plane into regions such that all points within one region have the same k nearest sites. The order-k abstract Voronoi diagram offers a unifying framework that represents a wide range of concrete order-k Voronoi diagrams. It is defined in terms of bisecting curves satisfying some simple combinatorial properties, rather than the geometric notions of sites and distance. In this paper we develop a randomized divide-and-conquer algorithm to compute the order-k abstract Voronoi diagram in expected O(kn1+ε) operations. For solving small sub-instances in the divide-and-conquer process, we also give two auxiliary algorithms with expected O(k2nlogn) and O(n22α(n)logn) time, respectively, where α(⋅) is the inverse of the Ackermann function. Our approach directly implies an O(kn1+ε)-time algorithm for several concrete order-k instances such as points in any convex distance, disjoint line segments or convex polygons of constant size in the Lp norms, and others. It also provides basic techniques that can enable the application of well-known random sampling techniques to the construction of Voronoi diagrams in the abstract setting and for non-point sites. © 2016 Elsevier B.V. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84985906123&doi=10.1016%2fj.comgeo.2016.08.004&partnerID=40&md5=edebfbce8f31961b0df9e43a31c408f5 https://scholars.lib.ntu.edu.tw/handle/123456789/624644 |
ISSN: | 09257721 | DOI: | 10.1016/j.comgeo.2016.08.004 | SDG/關鍵字: | Algorithms; Computational geometry; Concretes; Nearest neighbor search; Divide and conquer; Higher-order Voronoi diagrams; K-nearest neighbors; Randomized Algorithms; Voronoi diagrams; Graphic methods |
顯示於: | 電機工程學系 |
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