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An Efficient Method of Examining all Trees

Published online by Cambridge University Press:  12 September 2008

Ewa Kubicka
Ewa Kubicka
Affiliation:
Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, USA
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Abstract

In this paper, we present a techique for examining all trees of a given order. Our approach is based on the Beyer and Hedetniemi algorithm for generating all rooted trees of a given order and on the Wright, Richmond, Odlyzko and McKay algorithm for generating all free trees of a given order. In the introduction we describe these algorithms. We also give a precise evaluation of the average number of moves it takes to generate a rooted tree, which improves the upper bound given by Beyer and Hedetniemi. In the second section we present a new method of examining all trees which uses these generating algorithms. The last section contains two applications of the method introduced. The main result of the paper is that the average number of steps required by the proposed algorithm to examine a rooted tree is bounded by a constant independent of the order of a tree.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 5 , Issue 4 , December 1996 , pp. 403 - 413
Copyright
Copyright © Cambridge University Press 1996

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References

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