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Constructing Binary Space Partitions for Orthogonal Rectangles in Practice

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Algorithms — ESA’ 98 (ESA 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1461))

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Abstract

In this paper, we develop a simple technique for constructing a Binary Space Partition (BSP) for a set of orthogonal rectangles in ℝ3. Our algorithm has the novel feature that it tunes its performance to the geometric properties of the rectangles, e.g., their aspect ratios.

We have implemented our algorithm and tested its performance on real data sets. We have also systematically compared the performance of our algorithm with that of other techniques presented in the literature. Our studies show that our algorithm constructs BSPs of near-linear size and small height in practice, has fast running times, and answers queries efficiently. It is a method of choice for constructing BSPs for orthogonal rectangles.

A preliminary version of this paper appeared as a communication in the Proceedings of the 13th Annual ACM Symposium on Computational Geometry, 1997, pages 382–384.

This author is affiliated with Brown University. Support was provided in part by National Science Foundation research grant CCR-9522047 and by Army Research Office MURI grant DAAH04-96-1-0013.

Support was provided in part by National Science Foundation research grant CCR-93-01259, by Army Research Office MURI grant DAAH04-96-1-0013, by a Sloan fellowship, by a National Science Foundation NYI award and matching funds from Xerox Corp, and by a grant from the U.S.-Israeli Binational Science Foundation.

Support was provided in part by National Science Foundation research grant CCR-9522047, by Army Research Office grant DAAH04-93-G-0076, and by Army Research Office MURI grant DAAH04-96-1-0013.

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Author information

Authors and Affiliations

  1. Center for Geometric Computing Department of Computer Science, Duke University, Box 90129, Durham, NC, 27708-0129

    T. M. Murali, Pankaj K. Agarwal & Jeffrey Scott Vitter

Authors
  1. T. M. Murali
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  2. Pankaj K. Agarwal
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  3. Jeffrey Scott Vitter
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Editor information

Editors and Affiliations

  1. Dipartimento di Elettronica e Informatica, Università di Padova, via Gradenigo 6/A, I-35131, Padova, Italy

    Gianfranco Bilardi  & Geppino Pucci  & 

  2. Department of Electrical Engineering and Computer Science, The University of Illinois at Chicago, 851 South Morgan Street - 1009 SEO, Chicago, IL, 60607-7053, USA

    Gianfranco Bilardi

  3. Dipartimento di Matematica Applicata e Informatica, Università “Cá Foscari” di Venezia, via Torino 155, I-30173, Venezia Mestre, Italy

    Giuseppe F. Italiano

  4. Dipartimento di Matematica Pura e Applicata, Università di Padova, via Belzoni 7, I-35131, Padova, Italy

    Andrea Pietracaprina

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© 1998 Springer-Verlag Berlin Heidelberg

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Murali, T.M., Agarwal, P.K., Vitter, J.S. (1998). Constructing Binary Space Partitions for Orthogonal Rectangles in Practice. In: Bilardi, G., Italiano, G.F., Pietracaprina, A., Pucci, G. (eds) Algorithms — ESA’ 98. ESA 1998. Lecture Notes in Computer Science, vol 1461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68530-8_18

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  • DOI: https://doi.org/10.1007/3-540-68530-8_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64848-2

  • Online ISBN: 978-3-540-68530-2

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