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I/O-Efficient Well-Separated Pair Decomposition and Applications

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Abstract

We present an external-memory algorithm to compute a well-separated pair decomposition (WSPD) of a given point set S in ℝd in O(sort(N)) I/Os, where N is the number of points in S and sort(N) denotes the I/O-complexity of sorting N items. (Throughout this paper we assume that the dimension d is fixed.) As applications of the WSPD, we show how to compute a linear-size t-spanner for S within the same I/O-bound and how to solve the K-nearest-neighbour and K-closest-pair problems in O(sort(KN)) and O(sort(N+K)) I/Os, respectively.

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Authors and Affiliations

  1. Department of Computer Science, Duke University, Durham, NC 27708-0129, USA

    Sathish Govindarajan

  2. Heinz-Nixdorf-Institut and Department of Computer Science, University of Paderborn, Germany

    Tamas Lukovszki

  3. School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada

    Anil Maheshwari

  4. Faculty of Computer Science, Dalhousie University, 6050 University Avenue, Halifax, Nova Scotia, B3H 1W5, Canada

    Norbert Zeh

Authors
  1. Sathish Govindarajan
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  2. Tamas Lukovszki
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  3. Anil Maheshwari
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  4. Norbert Zeh
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Corresponding authors

Correspondence to Sathish Govindarajan, Tamas Lukovszki, Anil Maheshwari or Norbert Zeh.

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Govindarajan, S., Lukovszki, T., Maheshwari, A. et al. I/O-Efficient Well-Separated Pair Decomposition and Applications. Algorithmica 45, 585–614 (2006). https://doi.org/10.1007/s00453-005-1197-3

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  • DOI: https://doi.org/10.1007/s00453-005-1197-3

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