Subtree isomorphism is in random NC

Subtree Isomorphism Revisited

The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms are known, but for the general case truly subquadratic algorithms remain elusive. Our first result is a reduction from the Orthogonal Vectors problem to Sub...

Faster subtree isomorphism

We study the subtree isomorphism problem: Given trees H and G, find a subtree of G which is isomorphic to H or decide that there is no such subtree. We give an O( k1:5 logkn)time algorithm for this problem, where k and n are the number of vertices in H and G respectively. This improves over the O(k1:5n) algorithms of Chung and Matula. We also give a randomized (Las Vegas) O(min(k1:45n; kn1:43))...

Subtree Isomorphism is in DLOG for Nested Trees

This research note shows subtree isomorphism is in DLOG, and hence NC 2 , for nested trees. To our knowledge this result provides the rst interesting class of trees for which the problem is in a non-randomized version of NC. We also show that one can determine whether or not an arbitrary tree is a nested tree in DLOG.

On an Algorithm of Zemlyachenko for Subtree Isomorphism

Faster Algorithms for the Maximum Common Subtree Isomorphism Problem

The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is NP-hard in general graphs. Confining to trees renders polynomial time algorithms possible and is of fundamental importance for approaches on more general graph classes. Various v...