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Dynamic Compressed Hyperoctrees with Application to the N-body Problem

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1738))

Abstract

Hyperoctree is a popular data structure for organizing multidimensional point data. The main drawback ofthi s data structure is that its size and the run-time of operations supported by it are dependent upon the distribution of the points. Clarkson rectified the distributiondependency in the size of hyperoctrees by introducing compressed hyperoctrees. He presents an O(n log n) expected time randomized algorithm to construct a compressed hyperoctree. In this paper, we give three deterministic algorithms to construct a compressed hyperoctree in O(n log n) time, for any fixed dimension d. We present O(log n) algorithms for point and cubic region searches, point insertions and deletions. We propose a solution to the N-body problem in O(n) time, given the tree. Our algorithms also reduce the run-time dependency on the number ofdi mensions.

This research is supported in part by ARO under DAAG55-97-1-0368, NSF CAREER under CCR-9702991 and Sandia National Laboratories. The content ofthe information does not necessarily reflect the position or the policy of the U.S. federal government, and no official endorsement should be inferred.

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Author information

Authors and Affiliations

  1. Iowa State University, Ames, IA, 50011, USA

    Srinivas Aluru

  2. Syracuse University, Syracuse, NY, 13244, USA

    Fatih E. Sevilgen

Authors
  1. Srinivas Aluru
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  2. Fatih E. Sevilgen
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Chennai, 600036, India

    C. Pandu Rangan

  2. Institute of Mathematical Sciences C.I.T. Campus, Chennai, 600113, India

    V. Raman  & R. Ramanujam  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Aluru, S., Sevilgen, F.E. (1999). Dynamic Compressed Hyperoctrees with Application to the N-body Problem. In: Rangan, C.P., Raman, V., Ramanujam, R. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1999. Lecture Notes in Computer Science, vol 1738. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46691-6_2

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  • DOI: https://doi.org/10.1007/3-540-46691-6_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66836-7

  • Online ISBN: 978-3-540-46691-8

  • eBook Packages: Springer Book Archive

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