Subcaterpillar Isomorphism: Subtree Isomorphism Restricted Pattern Trees To Caterpillars

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.

Graph Isomorphism Restricted by Lists

The complexity of graph isomorphism (GraphIso) is a famous unresolved problem in theoretical computer science. For graphs G and H, it asks whether they are the same up to a relabeling. In 1981, Lubiw proved that list restricted graph isomorphism (ListIso) is NP-complete: for each u ∈ V (G), we are given a list L(u) ⊆ V (H) of possible images of u. After 35 years, we revive the study of this pro...

On an Algorithm of Zemlyachenko for Subtree Isomorphism