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Multidimensional divide-and-conquer

By Jon Louis Bentley

Communications of the ACM, Vol. 23 No. 4, Pages 214-229

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Most results in the field of algorithm design are single algorithms that solve single problems. In this paper we discuss multidimensional divide-and-conquer, an algorithmic paradigm that can be instantiated in many different ways to yield a number of algorithms and data structures for multidimensional problems. We use this paradigm to give best-known solutions to such problems as the ECDF, maxima, range searching, closest pair, and all nearest neighbor problems. The contributions of the paper are on two levels. On the first level are the particular algorithms and data structures given by applying the paradigm. On the second level is the more novel contribution of this paper: a detailed study of an algorithmic paradigm that is specific enough to be described precisely yet general enough to solve a wide variety of problems.

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