On the complexity of higher order abstract Voronoi diagrams
نویسندگان
چکیده
منابع مشابه
An Efficient Randomized Algorithm for Higher-Order Abstract Voronoi Diagrams
Given a set of n sites in the plane, the order-k Voronoi diagram is a planar subdivision such that all points in a region share the same k nearest sites. The order-k Voronoi diagram arises for the k-nearest-neighbor problem, and there has been a lot of work for point sites in the Euclidean metric. In this paper, we study order-k Voronoi diagrams defined by an abstract bisecting curve system tha...
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In this note we prove some facts about the number of segments of a bisector of two sites that are used in a higher order Voronoi diagram. CR Classification: F.2.1
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We study the complexity of higher-order Voronoi diagrams on triangulated surfaces under the geodesic distance, when the sites may be polygonal domains of constant complexity. More precisely, we show that on a surface defined by n triangles the sum of the combinatorial complexities of the order-j Voronoi diagrams of m sites, for j = 1, . . . , k, is O(kn + km+ knm), which is asymptotically tight...
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ژورنال
عنوان ژورنال: Computational Geometry
سال: 2015
ISSN: 0925-7721
DOI: 10.1016/j.comgeo.2015.04.008