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Acta Informatica

, Volume 13, Issue 2, pp 155–168 | Cite as

Efficient worst-case data structures for range searching

  • J. L. Bentley
  • H. A. Maurer
Article

Abstract

In this paper we investigate the worst-case complexity of range searching: preprocess N points in k-space such that range queries can be answered quickly. A range query asks for all points with each coordinate in some range of values, and arises in many problems in statistics and data bases. We develop three different structures for range searching in this paper. The first structure has absolutely optimal query time (which we prove), but has very high preprocessing and storage costs. The second structure we present has logarithmic query time and O(N1+2) preprocessing and storage costs, for any fixed ɛ>0. Finally we give a structure with linear storage, O(N ln N) preprocessing and O(Nɛ) query time.

Keywords

Information System Operating System Data Structure Communication Network Information Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bentley, J.L.: Multidimensional binary search trees used for associative searching. Comm. ACM 18, 509–517 (1975)CrossRefGoogle Scholar
  2. 2.
    Bentley, J.L.: Multidimensional Divide-Conquer. Carnegie Mellon University Computer Science Department Research Review, 1978, pp. 7–24Google Scholar
  3. 3.
    Bentley, J.L., Friedman. J.H.: Data structures for range searching. Comput. Surveys (in press 1980)Google Scholar
  4. 4.
    Knuth, D.E.: The Art of Computer Programming, vol.3. Reading, Mass.: Addison-Wesley 1973zbMATHGoogle Scholar
  5. 5.
    Lee, D.T., Wong, C.K.: Worst case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees. Acta Informatica 9, 23–29 (1977)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Maurer, H.A., Ottmann, Th.: Manipulating sets of points — a survey In: Graphen, Algorithmen, Datenstrukturen: Workshop 78, München-Wien: Hanser 1978Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • J. L. Bentley
    • 1
  • H. A. Maurer
    • 2
  1. 1.Departments of Computer Science and MathematicsCarnegie-Mellon UniversityPittsburghUSA
  2. 2.Institut für InformationsverarbeitungTechnische Universität GrazGrazAustria

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