Abstract
A parameterized binary search tree callediR tree is defined in this paper. A user is allowed to select a level of balance he desires. SR tree is a special case ofiR tree wheni=1. There are two new concepts in SR trees: (1) local balancing scheme that balances the tree locally; (2) consecutive storage for brother nodes that reduces pointer space. Although we may introduce empty nodes into the tree, we can show that only 1/8 of the nodes may be empty on the average, so it may still be advantageous in cases when record sizes are small. Insertion (and deletion) into SR trees can be done in timeh + O(1) whereh is the height of the tree. The average searching time for SR trees is shown to be 1.188 log2 k wherek is the number of keys. Generalization of the results of SR trees toiR in general is also given.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. E. Knuth,The Art of Computer Programming, Vol. 3, Addison-Wesley, Reading, Mass. (1973).
Th. Ottmann, H.-W. Six and D. Wood,The analysis of search trees: a survey, McMaster University, Computer Science Technical Report 80-CS-19, (1980).
W. M. Ching, Private communication.
A. C. Yao,On random 2–3 trees, Acta Informatica, 9 (1978), 159–170.
D. E. Knuth,The Art of Computer Programming, Vol. 1, Addison-Wesley, Reading, Mass. (1968).
E. M. Reingold, J. Nievergelt and N. Deo,Combinatorial Algorithms: Theory and Practice, Prentice-Hall, Englewood, New Jersey, (1977).
Author information
Authors and Affiliations
Additional information
The research of the first author was partially supported by a Research Initiation Grant from the University of Houston.
Rights and permissions
About this article
Cite this article
Huang, SH.S., Wong, C.K. Binary search trees with limited rotation. BIT 23, 436–455 (1983). https://doi.org/10.1007/BF01933619
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01933619