On the top-down evaluation of tree inclusion problem

We consider the following tree-matching problem: Given labelled, ordered trees P and T, can P be obtained from T by deleting nodes. Deleting a node v entails removing all edges incident to v and, if v has a parent u, replacing the edges from u to v by edges from u to the children of v. The best known algorithm for this problem needs O(|T|·|leaves(P)|) time and O(|leaves(P)|·min{DT,·|leaves(T)|} + |T| + |P|) space, where leaves(T) (resp. leaves(P)) stands for the set of the leaves of T (resp. P), and DT (resp. DP) for the height of T (resp. P). In this paper, we present a new algorithm that requires O(|T|·|leaves(P)|) time but only O(|T| + |P|) space.