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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)

A data structure is said to be self-adjusting if it dynamically reorganizes itself to adapt to the pattern of accesses. Efficiency is typically measured in terms of amortized complexity, that is, the average running time of an access over an arbitrary sequence of accesses. The best known example of such a data structure is Sleator and Tarjan's splay tree.… (More)

The well-separated pair decomposition (WSPD) is a fundamental structure in computational geometry. Given a set <i>P</i> of <i>n</i> points in <i>d</i>-dimensional space and a positive separation parameter <i>s</i>, an <i>s</i>-WSPD is a concise representation of all the <i>O</i>(<i>n</i><sup>2</sup>) pairs of <i>P</i> requiring only… (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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