Pattern matching in unordered trees

Abstract

The problem of comparison between unordered trees, i.e. trees for which the order among siblings is unimportant, is considered. The criterion for comparison is the distance as measured by a weighted sum of the costs of deletion, insertion, and relabel operations on tree nodes. Such comparisons may contribute to pattern recognition efforts in any field (e.g. genetics) where data can naturally be characterized by unordered trees. It is observed that the problem is NP-complete. An enumerative algorithm and several heuristics leading to approximate solutions are given. The algorithms are based on probabilistic hill climbing and bipartite matching techniques. The accuracy and time efficiency of the heuristics are evaluated by applying them to a set of trees transformed from industrial parts based on a previously proposed morphological model.<>