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International Symposium on Mathematical Foundations of Computer Science

MFCS 1992: Mathematical Foundations of Computer Science 1992 pp 1–13Cite as

On range searching with semialgebraic sets

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 629))

Abstract

Let P be a set of n points in ℝd (d a small fixed positive integer), and let Γ be a collection of subsets of ℝd, each of which is defined by a constant number of bounded degree polynomials. The Γ-range searching problem is defined as: Preprocess P into a data structure, so that all points of P lying in a given γ Γ can be counted (or reported) efficiently. Generalizing the simplex range searching techniques, we construct a data structure for Γ-range searching with nearly linear space and preprocessing time, which can answer a query in time O(n 1−1/b+δ), where d≤b≤ 2d−3 and δ>0 is an arbitrarily small constant. The actual value of b is related to the problem of partitioning arrangements of algebraic surfaces into constant-complexity cells.

Part of the work by P.A. was supported by National Science Foundation Grant CCR-91-06514. Part of the work by J.M. was supported by Humboldt Research Fellowship.

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Author information

Authors and Affiliations

  1. Computer Science Department, Duke University, 27706, Durham, NC

    Pankaj K. Agarwal

  2. Katedra aplikované matamatiky, Universita Karlova, Praha

    Jiří Matoušek

  3. Institut für Informatik, Freie Universität Berlin, Germany

    Jiří Matoušek

Authors
  1. Pankaj K. Agarwal
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  2. Jiří Matoušek
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Editor information

Ivan M. Havel Václav Koubek

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© 1992 Springer-Verlag Berlin Heidelberg

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Agarwal, P.K., Matoušek, J. (1992). On range searching with semialgebraic sets. In: Havel, I.M., Koubek, V. (eds) Mathematical Foundations of Computer Science 1992. MFCS 1992. Lecture Notes in Computer Science, vol 629. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-55808-X_1

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  • DOI: https://doi.org/10.1007/3-540-55808-X_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55808-8

  • Online ISBN: 978-3-540-47291-9

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