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·N 1−1/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·N 1−1/k) in both structures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bentley, J.L.: Multidimensional binary search trees used for associative searching. Comm. ACM 18, 509–517 (1975)
Bentley, J.L., Stanat, D.F.: Analysis of range searches in quad trees. Information Processing Lett. 3, 170–173 (1975)
Finkel, R.A., Bentley, J.L.: Quad trees: a data structure for retrieval on composite key. Acta Informat. 4, 1–9 (1974)
Knuth, D.E.: The art of computer programming, Vol. 3. New York: Addison-Wesley 1973
Rivest, R.L.: Partial-match retrieval algorithms. SIAM J. Comput. 5, 19–50 (1976)
Author information
Authors and Affiliations
Additional information
This author's research was supported in part by the National Science Foundation under grant MCS-76-17321 and in part by the Joint Service Electronics Program under contract DAAB-07-72-C-0259
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1007/BF00263763
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00263763