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We consider the problem of comparison between unordered trees, i.e., trees for which the order among siblings is unimportant. 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. In companion work, we have shown this problem to be NP-complete. This paper presents an efficient enumerative algorithm and several heuristics leading to approximate solutions. The algorithms are based on probabilistic hill climbing and bipartite matching techniques. The paper evaluates the accuracy and time efficiency of the heuristics by applying them to a set of trees transformed from industrial parts based on a previously proposed morphological model.< >