Showing papers on "Tree rearrangement published in 1984"
TL;DR: It appears that for a wide class of statistics on trees, pattern-matching has a linear expected time complexity (in contrast to a quadratic worst-case behaviour).
Abstract: This paper presents general results on the probabilities of occurrences of patterns in trees, which serve to analyze a commonly used pattern matching algorithm on trees. It appears that for a wide class of statistics on trees, pattern-matching has a linear expected time complexity (in contrast to a quadratic worst-case behaviour). The methods used are both combinatorial and analytic and prove useful in the evaluation of a wide class of tree algorithms.
74 citations
TL;DR: A distribution theory is developed from which the probability of finding, from a specified set of trees, a pair of trees with a given difference value is calculated, and it is indicated that it has biological relevance as it counts the different classes in the corresponding hierarchal systems.
Abstract: A significant problem in analysing the results from evolutionary tree building algorithms, and with comparing conflicting evolutionary hypotheses, has been to find a way to measure differences between trees whose pendant vertices (endpoints) are labelled. A number of different measures have been proposed, but none has been shown to be easy to calculate, biologically relevant and to have a known distribution. In this paper we analyse one measure of tree difference, show how it can be calculated easily, and indicate that it has biological relevance as it counts the different classes in the corresponding hierarchal systems. We then develop a distribution theory from which we calculate the probability of finding, from a specified set of trees, a pair of trees with a given difference value. A connection between this problem and an existing combinatorial problem is also given.
66 citations