Abstract
The purpose of this paper is to generalize the recent results on one-sided height-balanced trees (OSHB trees) to the case of one-sidedk-height-balanced trees, fork≥2. Surprisingly, this generalization leads to 0 (log2 n) insertion and deletion algorithms, which are simpler than those available for OSHB trees, and thus we claim this generalization is of independent interest.
Zusammenfassung
In dieser Arbeit werden die kürzlich erzielten Resultate über einseitig höhenbalanzierte Bäume (OSHB-Bäume) verallgemeinert auf den Fall einseitigk-höhenbalanzierter Bäume fürk≥2. Überraschenderweise führt die Verallgemeinerung zu 0(log2 n) Einfüge- und Entferne-Algorithmen, die einfacher sind als die entsprechenden Algorithmen für OSHB-Bäume. Wir glauben daher, daß diese Verallgemeinerung an sich interessant ist.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Brown, M. R.: A storage scheme for height-balanced trees. Information Processing Letters7, 5, 231–232 (1978).
Foster, C. C.: A generalization of AVL trees. Comm. ACM16, 513–517 (1973).
Hirschberg, D. S.: An insertion technique for one-sided height-balanced trees. Comm. ACM19, 8, 471–473 (1976).
Huddleston, C. S.: 0 (logN) insertion and deletion in one-sided height-balanced trees. Comp. Science Dept. University of Washington, Seattle, Washington 98195, TR No. 78-04-03 (April 1978).
Knuth, D. E.: The Art of Computer Programming, Vol. 3: Sorting and Searching. Reading, Mass.: Addison-Wesley 1973.
Kosaraju, R. S.: Insertions and deletions in one-sided height-balanced trees. Comm. ACM21, 226–227 (1978).
Luccio, F., Pagli, L.: On the height of height-balanced trees. IEEE Trans. Comput.C 25, 87–90 (1976).
Luccio, F., Pagli, L.: Rebalancing height-balanced trees. IEEE Trans. Comput.C 27, 386–396 (1978).
Ottmann, Th., Wood, D.: Deletion in one-sided height-balanced search trees. Intern. J. Computer Math.6, 265–271 (1978).
Ottmann, Th., Six, H. W., Wood, D.: Right brother trees. Comm. ACM21, 769–776 (1978).
Räihä, K.-J.: An 0 (logn) insertion algorithm for one-sided height-balanced binary search trees. Department of Computer Science, University of Helsinki, Finland, Report A-1977-9.
Zweben, S. H., McDonald, M. A.: An optimal method for deletion in one-sided height-balanced trees. Comm. ACM21, 441–445 (1978).
Zweben, S. H.: An optimal insertion method for one-sided height-balanced trees. Department of Computer and Information Science, Ohio State University, Columbus, Ohio (October 1977).
Author information
Authors and Affiliations
Additional information
The third author was partially supported under the auspices of the University of Karlsruhe and partially supported under a National Research Council of Canada Grant No. A-7700.
Rights and permissions
About this article
Cite this article
Ottmann, T., Six, H.W. & Wood, D. One-sided k-height-balanced trees. Computing 22, 283–290 (1979). https://doi.org/10.1007/BF02265310
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02265310