A Linear-Space Top-Down Algorithm for Tree Inclusion Problem

We consider the following tree-matching problem: Given labeled, 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{D
_T
, |leaves(T)|} + |T| + |P|) space, where leaves(T) (resp. leaves(P)) stands for the set of the leaves of T (resp. P), and D
_T
(resp. D
_P
) for the height of T (resp. P). In this paper, we present an efficient algorithm that requires O(|T|.|leaves(P)|) time and O(|T| + |P|) space.