Patterns and pattern-matching in trees: An analysis

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