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The Computer Journal 1983 26(2):106-108; doi:10.1093/comjnl/26.2.106
© 1983 by British Computer Society
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Height-Ratio-Balanced Trees

G. H. Gonnet1 *, H. J. Olivié2 § and D. Wood1 ¶

1 Data Structuring Group, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada, 2 Unit for Mathematics and Computer Science, IHAM, Paardenmarkt 94, Antwerp, Belgium

We introduce a new class of binary search trees, the height-ratio-balanced binary search trees, as the height based analogy of weight (–ratio) balanced binary search trees. They form a proper subclass of the class of binary search trees, but not a logarithmic one, indeed an n node height-ratio balanced tree of order {alpha},0≤{alpha}≤1/3, has a worse case height of µmgr]eµ+0(1), where µ=(–2ln({alpha}/(1-a))ln(n)}1/2. This result indicates that these naturally defined trees should not be used to implement the DICTIONARY operations, in practical situations.

Received December 1981.

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

§ Unit for Mathematics and Computer Science, IHAM, Paardenmarkt 94 B-2000, Antwerp, Belgium

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


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