Prof. Avraham Melkman

The largest common subtree problem is to find a bijective mapping between subsets of nodes of two input rooted trees of maximum cardinality or weight that preserves labels and ancestry relationship. This problem is known to be NP-hard for unordered trees. In this paper, we consider a restricted unordered case in which the maximum outdegree of a common subtree is bounded by a constant D. We present an O(n^D) time algorithm where n is the maximum size of two input trees, which improves a previous O(n^2D) time algorithm. We also prove that this restricted problem is W[1]-hard for parameter D.