Some average measures in m-ary search trees

doi:10.1016/0020-0190(87)90215-8

Information Processing Letters

Volume 25, Issue 6, 26 July 1987, Pages 375-381

https://doi.org/10.1016/0020-0190(87)90215-8 Get rights and content

Abstract

We obtain the expected number of comparisons for an unsuccessful search and the average storage performance of the m-ary search tree under three different storage methods. We model the trees as being built from uniform, random keys.

References (7)

B. Eisenbarth et al.
The theory of fringe analysis and its application to 2–3 trees and B-trees
Inform. and Control
(1982)
P.V. Poblete et al.
The analysis of a fringe heuristic for binary search trees
J. Algorithms
(1985)
R.A. Baeza-Yates
Analysis of algorithms in search trees

There are more references available in the full text version of this article.

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^∗: Present affiliation: Data Structuring Group, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.

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Some average measures in m-ary search trees

Abstract

Inform. and Control

J. Algorithms

Analysis of algorithms in search trees