On agreement forests

A Unifying View on Approximation and FPT of Agreement Forests

We provide a unifying view on the structure of maximum (acyclic) agreement forests of rooted and unrooted phylogenies. This enables us to obtain linearor O(n logn)-time 3-approximation and improved fixed-parameter algorithms for the subtree prune and regraft distance between two rooted phylogenies, the tree bisection and reconnection distance between two unrooted phylogenies, and the hybridizat...

Approximation Algorithms for Nonbinary Agreement Forests

Given two rooted phylogenetic trees on the same set of taxa X, the Maximum Agreement Forest problem (MAF) asks to find a forest that is, in a certain sense, common to both trees and has a minimum number of components. The Maximum Acyclic Agreement Forest problem (MAAF) has the additional restriction that the components of the forest cannot have conflicting ancestral relations in the input trees...

Computing hybridization networks using agreement forests

Fixed-Parameter and Approximation Algorithms for Maximum Agreement Forests

We present new and improved approximation and FPT algorithms for computing rooted and unrooted maximum agreement forests (MAFs) of pairs of phylogenetic trees. Their sizes correspond to the subtree-prune-and-regraft distances and the tree-bisection-and-reconnection distances of the trees, respectively. We also provide the first bounded search tree FPT algorithm for computing rooted maximum acyc...

Computing a Relevant Set of Nonbinary Maximum Acyclic Agreement Forests

There exist several methods dealing with the reconstruction of rooted phylogenetic networks explaining different evolutionary histories given by rooted binary phylogenetic trees. In practice, however, due to insufficient information of the underlying data, phylogenetic trees are in general not completely resolved and, thus, those methods can often not be applied to biological data. In this work...