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Well Separated Pair Decomposition

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  • First Online:
Encyclopedia of Algorithms

  • 146 Accesses

Years and Authors of Summarized Original Work

  • 1995; Callahan, Kosaraju

Problem Definition

Well-separated pair decomposition, introduced by Callahan and Kosaraju [4], has found numerous applications in solving proximity problems for points in the Euclidean space. A pair of point sets (A,  B) is c well separated if the distance between A and B is at least c times the diameters of both A and B. A well-separated pair decomposition of a point set consists of a set of well-separated pairs that “cover” all the pairs of distinct points, i.e., any two distinct points belong to the different sets of some pair. Callahan and Kosaraju [4] showed that for any point set in a Euclidean space and for any constant c ≥ 1, there always exists a c-well-separated pair decomposition (c-WSPD) with linearly many pairs. This fact has been very useful for obtaining nearly linear-time algorithms for many problems, such as computing k-nearest neighbors, N-body potential fields, geometric spanners, approximate...

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Authors and Affiliations

  1. Institute for Computer Science, University of Bonn, Bonn, Germany

    Rolf Klein

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  1. Rolf Klein
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Correspondence to Rolf Klein .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Klein, R. (2016). Well Separated Pair Decomposition. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_479

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