The effect of updates in binary search trees

Authors:
J C Culberson
Affiliations:
Data Structuring Group, Department of Computer Science, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
Venue:
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Year:
1985

Citing 4
Cited 1

The art of computer programming, volume 1 (3rd ed.): fundamental algorithms

The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Some Combinatorial Properties of Certain Trees With Applications to Searching and Sorting

Journal of the ACM (JACM)
An empirical study of insertion and deletion in binary search trees

Communications of the ACM
Deletion in binary storage trees.

Deletion in binary storage trees.

Randomized binary search trees

Journal of the ACM (JACM)

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Abstract

If a binary search tree is created by inserting N keys in random order using the usual insertion algorithm, then it is well known that the average search path is about 1.4lgN. However, if deletions, using the frequently recommended Hibbard's algorithm, are interspersed with the insertions, then virtually nothing has been proven except for Knuth and Jonassen's very difficult, but complete, analysis of the case N = 3. In this paper it is shown that after a sufficient number of updates the average search path is &thgr;(N1/2). An improved algorithm given by Knuth is shown to have the same asymptotic behavior.