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Acta Informatica

, Volume 9, Issue 1, pp 23–29 | Cite as

Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees

  • D. T. Lee
  • C. K. Wong
Article

Summary

Given a file of N records each of which has k keys, the worst-case analysis for the region and partial region queries in multidimensional binary search trees and balanced quad trees are presented. It is shown that the search algorithms proposed in [1, 3] run in time O(k·N1−1/k) for region queries in both tree structures. For partial region queries with s keys specified, the search algorithms run at most in time O(s·N1−1/k) in both structures.

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)Google Scholar
  2. 2.
    Bentley, J.L., Stanat, D.F.: Analysis of range searches in quad trees. Information Processing Lett. 3, 170–173 (1975)Google Scholar
  3. 3.
    Finkel, R.A., Bentley, J.L.: Quad trees: a data structure for retrieval on composite key. Acta Informat. 4, 1–9 (1974)Google Scholar
  4. 4.
    Knuth, D.E.: The art of computer programming, Vol. 3. New York: Addison-Wesley 1973Google Scholar
  5. 5.
    Rivest, R.L.: Partial-match retrieval algorithms. SIAM J. Comput. 5, 19–50 (1976)Google Scholar

Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • D. T. Lee
    • 1
  • C. K. Wong
    • 2
  1. 1.Department of Computer Science and the Coordinated Science LaboratoryUniversity of IllinoisUrbana-ChampaignUSA
  2. 2.IBM Thomas J. Watson Research CenterYorktown HeightsUSA

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