A New Top-Down Algorithm for Tree Inclusion

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. This problem has a lot of applications in the computer engineering, such as XML tree pattern query evaluation, video content-based retrieval, as well as in computational biology, and data mining. 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 number 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 a new algorithm that requires O(|T|·min{D_P, |leaves(P)|}) time and O(|T| + |P|) space.