Skip Navigation

The Computer Journal 1989 32(1):68-75; doi:10.1093/comjnl/32.1.68
© 1989 by British Computer Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (4)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Culberson, J.
Right arrow Articles by Munro, J. I.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

Explaining the Behaviour of Binary Search Trees Under Prolonged Updates: A Model and Simulations

J. Culberson1 * and J. I. Munro2 §

1 Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2E7, 2 Data Structuring Group, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

In this paper we present an extensive study into the long-term behaviour of binary search trees subjected to updates using the usual deletion algorithms taught in introductory textbooks. We develop a model of the behaviour of such trees which leads us to conjecture that the asymptotic average search path length is {Theta}(N1/2). We present results of large simulations which strongly support this conjecture. However, introducing a simple modification to ensure symmetry in the algorithms, the model predicts no such long-term deterioration. Simulations in fact indicate that asymptotically the average path length of such trees is less than the 1.386...log2 N average path length of trees generated from random insertion sequences.

Received December 1987. revised May 1988.

This work was done in part while the first author was at the University of Waterloo. This work was supported by an NSERC '67 Science Scholarship, Grant A-8053 and grant A-8237, and by the Information Technology Research Centre of Ontario.

* Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2E7

§ Data Structuring Group, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.