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Weighted orthogonal linear L ∞-approximation and applications

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Algorithms and Data Structures (WADS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 382))

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Abstract

Let S={s 1, s 2,...,s n } be a set of sites in E d, where every site s i has a positive real weight ω i . This paper gives an algorithm to find a weighted orthogonal L ∞-approximation hyperplane for S. The algorithm is shown to require O(nlogn) time and O(n) space for d=2, and O(n [d/2+1]) time and O(n [(d+1)/2]) space for d>2. The L ∞-approximation algorithm will be adapted to solve the problem of finding the width of a set of n points in E d, and the problem of finding a stabbing hyperplane for a set of n hyperspheres in E d with varying radii. The time and space complexities of the width and stabbing algorithms are seen to be the same as those of the L ∞-approximation algorithm.

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Author information

Authors and Affiliations

  1. School of Computer Science, McGill University, H3A 2A7, Montréal, Québec, Canada

    Michael E. Houle & Jean-Marc Robert

  2. Department of Computer Science and Communication Engineering, Kyushu University, 812, Fukuoka, Japan

    Hiroshi Imai

  3. Information Science Center, Kyushu Institute of Technology Iizuka, 820, Fukuoka, Japan

    Keiko Imai

Authors
  1. Michael E. Houle
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  2. Hiroshi Imai
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  3. Keiko Imai
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  4. Jean-Marc Robert
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Editor information

F. Dehne J. -R. Sack N. Santoro

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© 1989 Springer-Verlag Berlin Heidelberg

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Houle, M.E., Imai, H., Imai, K., Robert, JM. (1989). Weighted orthogonal linear L ∞-approximation and applications. In: Dehne, F., Sack, J.R., Santoro, N. (eds) Algorithms and Data Structures. WADS 1989. Lecture Notes in Computer Science, vol 382. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51542-9_16

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  • DOI: https://doi.org/10.1007/3-540-51542-9_16

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51542-5

  • Online ISBN: 978-3-540-48237-6

  • eBook Packages: Springer Book Archive

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