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Succinct Data Structures for Approximating Convex Functions with Applications

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Discrete and Computational Geometry (JCDCG 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2866))

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Abstract

We study data structures for providing ε-approximations of convex functions whose slopes are bounded. Since the queries are efficient in these structures requiring only \(O\left(\log(1/\varepsilon)+\log\log n\right)\) time, we explore different applications of such data structures to efficiently solve problems in clustering and facility location. Our data structures are succinct using only O((1/ε)log2(n)) bits of storage. We show that this is optimal by providing a matching lower bound showing that any data structure providing such an ε-approximation requires at least Ω((1/ε)log2(n)) bits of storage.

This research was partly supported by NSERC.

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Author information

Authors and Affiliations

  1. School of Computer Science, Carleton University, Ottawa, Canada, K1S 5B6

    Prosenjit Bose & Pat Morin

  2. School of Computer Science, McGill University, Montréal, Canada, H3A 2K6

    Luc Devroye

Authors
  1. Prosenjit Bose
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  2. Luc Devroye
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  3. Pat Morin
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Shibuya-ku Tokio, Japan

    Jin Akiyama

  2. Ibaraki University, Nakanarusawa, Hitachi, 316-8511, Ibaraki, Japan

    Mikio Kano

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© 2003 Springer-Verlag Berlin Heidelberg

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Bose, P., Devroye, L., Morin, P. (2003). Succinct Data Structures for Approximating Convex Functions with Applications. In: Akiyama, J., Kano, M. (eds) Discrete and Computational Geometry. JCDCG 2002. Lecture Notes in Computer Science, vol 2866. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44400-8_10

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  • DOI: https://doi.org/10.1007/978-3-540-44400-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20776-4

  • Online ISBN: 978-3-540-44400-8

  • eBook Packages: Springer Book Archive

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