On the Maximum Common Embedded Subtree Problem for Ordered Trees

The maximum common embedded subtree problem, which generalizes the minor containment problem on trees, is reduced for ordered trees to a variant of the longest common subsequence problem. While the maximum common embedded subtree problem is known to be APX-hard for unordered trees, an exact solution for ordered trees can be found in polynomial time. In this paper, the longest common balanced sequence problem, and thus the maximum common embedded subtree problem, are solved in O(n1n2 min(d1, 1)min(d2, 2)) time, on ordered trees with n1 and n2 nodes, of depth d1 and d2, and with 1 and 2 leaves.