Approximation and Special Cases of Common Subtrees and Editing Distance

Given two rooted, labeled, unordered trees, the common subtree problem is to find a bijective matching between subsets of vertices of the trees of maximum cardinality which preserves labels and ancestry relationship. The tree editing distance problem is to determine the least cost sequence of additions, deletions and changes that converts a tree into another given tree. Both problems are known to be hard to approximate within some constant factor in general.