An improved bound on the Maximum Agreement Subtree problem

TL;DR

This paper enhances the theoretical lower bounds for the Maximum Agreement Subtree problem, showing that two binary trees with n leaves share a large common subtree of size proportional to log log n.

Contribution

The authors establish a new lower bound on the size of the maximum agreement subtree, improving previous results in the extremal case.

Findings

Two binary trees on n leaves have a common subtree with at least c log log n leaves.

The bound is tight up to constant factors for large n.

The result advances understanding of tree similarity measures.

Abstract

We improve the lower bound on the extremal version of the Maximum Agreement Subtree problem. Namely we prove that two binary trees on the same $n$ leaves have subtrees with the same $\geq c\log\log n$ leaves which are homeomorphic, such that homeomorphism is identity on the leaves.