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In this paper, we introduce a simple, randomized dynamic data structure for storing multidimensional point sets, called a <i>quadtreap</i>. This data structure is a randomized, balanced variant of a quadtree data structure. In particular, it defines a hierarchical decomposition of space into cells, which are based on hyperrectangles of bounded aspect ratio,(More)
The problem of maintaining geometric structures for points in motion has been well studied over the years. Much theoretical work to date has been based on the assumption that point motion is continuous and predictable, but in practice, motion is typically presented incrementally in discrete time steps and may not be predictable. We consider the problem of(More)
Range searching is a widely-used method in computational geometry for efficiently accessing local regions of a large data set. Typically, range searching involves either counting or reporting the points lying within a given query region, but it is often desirable to compute statistics that better describe the structure of the point set lying within the(More)
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