https://scholars.lib.ntu.edu.tw/handle/123456789/624651
Title: | A Randomized Divide and Conquer Algorithm for Higher-Order Abstract Voronoi Diagrams | Authors: | Bohler C Liu C.-H Papadopoulou E Zavershynskyi M. CHIH-HUNG LIU |
Keywords: | Abstract Voronoi Diagram; Divide and Conquer; Higher-Order Voronoi Diagram; Randomized Algorithm | Issue Date: | 2014 | Journal Volume: | 8889 | Start page/Pages: | 27-37 | Source: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Abstract: | Given a set of 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 is defined in terms of bisecting curves satisfying some simple combinatorial properties, rather than the geometric notions of sites and distance, and it represents a wide class of order-k concrete Voronoi diagrams. In this paper we develop a randomized divide-andconquer 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 sub-algorithms with expected O(k2n log n) and O(n22α(n) log n) time, respectively. This directly implies an O(kn1+ε)-time algorithm for several concrete order-k instances such as points in any convex distance, disjoint line segments and convex polygons of constant size in the Lp norm, and others. © Springer International Publishing Switzerland 2014. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-84921648246&doi=10.1007%2f978-3-319-13075-03&partnerID=40&md5=0ee1e52de7b5570adfe9194e280d0fb7 https://scholars.lib.ntu.edu.tw/handle/123456789/624651 |
ISSN: | 03029743 | DOI: | 10.1007/978-3-319-13075-03 | SDG/Keyword: | Computational geometry; Concretes; Graphic methods; Combinatorial properties; Divide and conquer; Divide-and-conquer algorithm; Higher-order Voronoi diagrams; Order-k Voronoi diagrams; Randomized Algorithms; Time algorithms; Voronoi diagrams; Algorithms |
Appears in Collections: | 電機工程學系 |
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