Decomposition algorithms for the tree edit distance problem

We study the behavior of dynamic programming methods for the tree edit distance problem, such as [P. Klein, Computing the edit-distance between unrooted ordered trees, in: Proceedings of 6th European Symposium on Algorithms, 1998, p. 91-102; K. Zhang, D. Shasha, SIAM J. Comput. 18 (6) (1989) 1245-1262]. We show that those two algorithms may be described as decomposition strategies. We introduce the general framework of cover strategies, and we provide an exact characterization of the complexity of cover strategies. This analysis allows us to define a new tree edit distance algorithm, that is optimal for cover strategies.