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An Intoductory Tutorial on Kd-Trees
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(1991)

This paper considers the expected number of hyperrectangles corresponding to leaf nodes which will provably need to be searched. Such hyperrectangles intersect the volume enclosed by a hypersphere centered on the query point whose surface passes through the nearest neighbour. For example, in Figure 6.5 the hypersphere (in this 6-9 Figure 6.5 Generally during a nearest neighbour search only a few leaf nodes need to be inspected.
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