Multidimensional divide-and-conquer

TLDR

Most results in algorithm design are single algorithms that solve single problems. The paper presents a detailed study of multidimensional divide‑and‑conquer, a paradigm that can be instantiated in many ways to produce algorithms and data structures for multidimensional problems, and outlines its two levels of contribution. The authors introduce multidimensional divide‑and‑conquer as a paradigm that can be instantiated in many ways to yield algorithms and data structures for multidimensional problems. Using this paradigm, the authors provide best‑known solutions to problems such as ECDF, maxima, range searching, closest pair, and all nearest neighbor, and present the specific algorithms and data structures derived from it.

Abstract

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.