Alignment of Trees - An Alternative to Tree Edit

In this paper, we propose the alignment of trees as a measure of the similarity between two labeled trees. Both ordered and unordered trees are considered. An algorithm is designed for ordered trees. The time complexity of this algorithm is O( IT a I . ITz l . (deg(T I ) + degqT2))2). where I Til is the number of nodes in Ti and de6(T~) is the degree of T i, i -I. 2. The algorithm is faster than the best known algorithm for tree edit when deg(Tt) and deg(Tzl are smaller than the depths of T t and Tz. For unordered trees, we show that the alignment problem can be solved in polynomial time if the trees have a bounded degree and becomes MAX SNP-hard if one of the trees is allowed to have an arbitrary degree. In contrast, the edit problem for unordered trees is MAX SNP-hard even if both trees have a bounded degree (Zhang and Jiang, 1994). Finally, multiple alignment of trees is discussed.