Faster 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...

Induced Subtrees in Interval Graphs

The Induced Subtree Isomorphism problem takes as input a graph G and a tree T , and the task is to decide whether G has an induced subgraph that is isomorphic to T . This problem is known to be NP-complete on bipartite graphs, but it can be solved in polynomial time when G is a forest. We show that Induced Subtree Isomorphism can be solved in polynomial time when G is an interval graph. In cont...

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

Fast subtree kernels on graphs

In this article, we propose fast subtree kernels on graphs. On graphs with n nodes and m edges and maximum degree d, these kernels comparing subtrees of height h can be computed in O(mh), whereas the classic subtree kernel by Ramon & Gärtner scales as O(n4h). Key to this efficiency is the observation that the Weisfeiler-Lehman test of isomorphism from graph theory elegantly computes a subtree k...