Abstract
The selection problem asks for the kth largest or smallest element in a set S. In general, selection takes linear time, but if the set is constrained so that some relations between elements are known, sublinear-time selection is sometimes possible. We present an algorithm that selects the kth largest or smallest element from a Cartesian sum in O ( n log n) time and extend this result to select L ∞-interdistances in R d in O( d n log d−1 n) time. The algorithm is based on a general technique o f Megiddo and improved by Cole, and it is the first algorithm for a multidimensional interdistance selection problem with an O( n log O(1) n ) running time.
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