On the algorithm of Berztiss for tree pattern matching

The tree pattern matching problem over labeled trees is addressed in This work. Several tree pattern matching algorithms are known which are based on the decomposition of the pattern into strings, with each string representing a root-to-leaf path. Among these, Alfs T. Berztiss gave a simple tree pattern matching algorithm which remained unknown to the research community. The tree pattern matching algorithm of Berztiss is reviewed, its correctness is established, and its complexity is shown to be O(mn) time and space in the worst case and O(n) on the average, where n is the text size and m is the pattern size.