Alignment of trees — an alternative to tree edit

Abstract

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(| T 1|·| T 2·(deg( T 1) + deg( T 2)) 2), where | T 1| is the number of nodes in T 1 and deg( T 1) is the degree of T 1, i = 1.2. The algorithm is faster than the best known algorithm for tree edit when deg( T 1) and deg( T 2) are smaller than the depths of T 1 and T 2. 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.