On the Maximum Agreement Subtree Conjecture for Balanced Trees

Solving the Maximum Agreement SubTree and the Maximum Compatible Tree Problems on Many Bounded Degree Trees

Given a set of leaf-labeled trees with identical leaf sets, the well-known Maximum Agreement SubTree problem (MAST) consists of finding a subtree homeomorphically included in all input trees and with the largest number of leaves. Its variant called Maximum Compatible Tree (MCT) is less stringent, as it allows the input trees to be refined. Both problems are of particular interest in computation...

Approximating the Maximum Isomorphi Agreement Subtree is

An O(n log n) Algorithm for the Maximum Agreement Subtree Problem for Binary Trees

The Maximum Agreement Subtree problem is the following: given two rooted trees whose leaves are drawn from the same set of items (e.g., species), find the largest subset of these items so that the portions of the two trees restricted to these items are isomorphic. We consider the case which occurs frequently in practice, i.e., the case when the trees are binary, and give an O(n logn) time algor...

On the Maximum Common Embedded Subtree Problem for Ordered Trees

The maximum common embedded subtree problem, which generalizes the minor containment problem on trees, is reduced for ordered trees to a variant of the longest common subsequence problem. While the maximum common embedded subtree problem is known to be APX-hard for unordered trees, an exact solution for ordered trees can be found in polynomial time. In this paper, the longest common balanced se...

Bounds on the Expected Size of the Maximum Agreement Subtree

We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question posed in earlier work. Determining tight upper and lower bounds remains an open problem.