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Binary space partitions for sets of hyperrectangles

  • Algorithms
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Algorithms, Concurrency and Knowledge (ACSC 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1023))

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Abstract

In this paper we prove the existence of binary space partitions (BSPs) with linear size for sets of axis-parallel boxes in three dimensional space under certain conditions that are often satisfied in practical situations. In particular, we give an O(n log n) time algorithm to construct a BSP tree with linear size for a set S of axis-parallel boxes where the ratio between the lengths of the longest and the shortest edges of boxes in S is bounded by a constant. The BSP tree constructed is balanced if S has a constant profile.

In view of the lower bound of Ω(n3/2) for the size of BSPs for set of n line segments (or boxes) in ℝ3, this is the first class of high dimensional objects that are found, for which linear size BSPs exist. We generalize the results for sets of hyperrectangles in dimension greater than three and extend our method also for a useful class of d-dimensional fat objects. All the algorithms for constructing linear size binary space partitions presented in this paper are simple enough to be favorable for implementations.

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Authors and Affiliations

  1. Swiss Federal Institute of Technology (ETH) Zürich, ETH Zentrum, CH-8092, Zürich, Switzerland

    Viet Hai Nguyen & Peter Widmayer

Authors
  1. Viet Hai Nguyen
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  2. Peter Widmayer
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Kanchana Kanchanasut Jean-Jacques Lévy

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© 1995 Springer-Verlag Berlin Heidelberg

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Nguyen, V.H., Widmayer, P. (1995). Binary space partitions for sets of hyperrectangles. In: Kanchanasut, K., Lévy, JJ. (eds) Algorithms, Concurrency and Knowledge. ACSC 1995. Lecture Notes in Computer Science, vol 1023. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60688-2_35

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  • DOI: https://doi.org/10.1007/3-540-60688-2_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60688-8

  • Online ISBN: 978-3-540-49262-7

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