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Three-Dimensional Layers of Maxima

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Book cover Algorithms — ESA 2002 (ESA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2461))

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Abstract

We present an O(n log n)-time algorithm to solve the threedimensional layers-of-maxima problem, an improvement over the prior O(n log n log log n)-time solution. A previous claimed O(n log n)-time solution due to Atallah, Goodrich, and Ramaiyer [SCG’94] has technical flaws. Our algorithm is based on a common framework underlying previous work, but to implement it we devise a new data structure to solve a special case of dynamic planar point location in a staircase subdivision. Our data structure itself relies on a new extension to dynamic fractional cascading that allows vertices of high degree in the control graph.

Supported by DARPA Grant F30602-00-2-0509 and NSF Grant CCR-0098068.

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Author information

Authors and Affiliations

  1. AT&T Labs, Shannon Laboratory, 180 Park Ave., Florham Park, NJ, 07932

    Adam L. Buchsbaum

  2. Dept. of Information & Computer Science, University of California, Irvine, CA, 92697-3425

    Michael T. Goodrich

Authors
  1. Adam L. Buchsbaum
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  2. Michael T. Goodrich
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Editor information

Editors and Affiliations

  1. Fakultät II: Mathematik und Naturwissenschaften, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Rolf Möhring

  2. Department of Mathematics and Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Rajeev Raman

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© 2002 Springer-Verlag Berlin Heidelberg

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Buchsbaum, A.L., Goodrich, M.T. (2002). Three-Dimensional Layers of Maxima. In: Möhring, R., Raman, R. (eds) Algorithms — ESA 2002. ESA 2002. Lecture Notes in Computer Science, vol 2461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45749-6_26

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  • DOI: https://doi.org/10.1007/3-540-45749-6_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44180-9

  • Online ISBN: 978-3-540-45749-7

  • eBook Packages: Springer Book Archive

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