Constrained tree inclusion

The tree matching problem is considered of given labeled trees P and T, determining if the pattern tree P can be obtained from the text tree T by deleting degree-one and degree-two nodes and, in the case of unordered trees, by also permuting siblings. The constrained tree inclusion problem is more sensitive to the structure of the pattern tree than the general tree inclusion problem. Further, it can be solved in polynomial time for both unordered and ordered trees. Algorithms based on the subtree homeomorphism algorithm of (Chung, 1987) are presented that solve the constrained tree inclusion problem in O(m1.5n) time on unordered trees with m and n nodes, and in O(mn) time on ordered trees, using O(mn) additional space. These algorithms can be improved using results of (Shamir and Tsur, 1999) to run in O((m1.5/ logm)n) and O((m/logm)n) time, respectively