Subtree Isomorphism Revisited

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))...

Planar Subgraph Isomorphism Revisited

The problem of Subgraph Isomorphism is defined as follows: Given a pattern H and a host graph G on n vertices, does G contain a subgraph that is isomorphic to H? Eppstein [SODA 95, J’GAA 99] gives the first linear time algorithm for subgraph isomorphism for a fixed-size pattern, say of order k, and arbitrary planar host graph, improving upon the O(n √ )-time algorithm when using the “Color-codi...

The Wirthmüller Isomorphism Revisited

We show how the formal Wirthmüller isomorphism theorem proven in [2] simplifies the proof of the Wirthmüller isomorphism in equivariant stable homotopy theory. Other examples from equivariant stable homotopy theory show that the hypotheses of the formal Wirthmüller and formal Grothendieck isomorphism theorems in [2] cannot be weakened.

On an Algorithm of Zemlyachenko for Subtree Isomorphism