Nearest-Neighbor Queries with Well-Spaced Points
Voronoi Diagrams in Science and Engineering（2010）
摘要
We assume we are given a set of points that have the property that their Voronoi diagram---restricted to some suitable bounding box---consists of only fat cells. We call such points \emph{well-spaced points}. We give a linear-sized data structure for finding the nearest neighbor to a query point among well-spaced points in \(O(\log n)\) time. We further show how to extend the results to higher dimensions. Finally, we show how to find the Voronoi diagram of these points in \(O(n \log n)\) time in 3 dimensions.
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关键词
well-spaced point,well-spaced points,nearest-neighbor queries,linear-sized data structure,query point,fat cell,nearest neighbor,log n,voronoi diagram,higher dimension,computational modeling,computer networks,construction industry,algorithm design and analysis,data structures,euclidean distance,data structure,operating systems,computational geometry
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