Approximation Algorithms for the Largest Common Subtree Problem

The largest common subtree problem is to nd a largest tree which occurs as a common subgraph in a given collection of trees. Let n denote the number of vertices in the largest tree in the collection. We show that in the case of bounded degree trees, it is possible to achieve an approximation ratio of O(n(log logn)= log n). For unbounded degree trees, we give an algorithm with approximation ratio O(n(log logn)= log n) when the trees are unlabeled. An approximation ratio of O(n(log logn)= log n) is also achieved for the case of labeled unbounded degree trees provided the number of distinct labels is O(log n).