Results

**1 - 3**of**3**### Hybridization Number on Three Trees

, 2014

"... Phylogenetic networks are leaf-labelled directed acyclic graphs that are used to describe non-treelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum of all indegrees minus the number of nodes plus one. The Hy ..."

Abstract
- Add to MetaCart

Phylogenetic networks are leaf-labelled directed acyclic graphs that are used to describe non-treelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum of all indegrees minus the number of nodes plus one. The Hybridization Number problem takes as input a collection of phylogenetic trees and asks to construct a phylogenetic network that contains an embedding of each of the input trees and has a smallest possible hybridization number. We present an algorithm for the Hybridization Number problem on three binary phylogenetic trees on n leaves, which runs in time O(ckpoly(n)), with k the hybridization number of an optimal network and c some positive constant. For the case of two trees, an algorithm with running time O(3.18kn) was proposed before whereas an algorithm with running time O(ckpoly(n)) for more than two trees had prior to this article remained elusive. The algorithm for two trees uses the close connection to acyclic agreement forests to achieve a linear exponent in the running time, while previous algorithms for more than two trees (explicitly or implicitly) relied on a brute force search through all possible underlying network topologies, leading to running times that are not O(ckpoly(n)), for any c. The connection to acyclic agreement forests is much weaker for

### Agreement Forests ยท Bounded Search

"... Abstract It is a known fact that given two rooted binary phylogenetic trees the concept of maximum acyclic agreement forests is sufficient to com-pute hybridization networks with minimum hybridization number. In this work we demonstrate by, first, presenting an algorithm and, second, showing its cor ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract It is a known fact that given two rooted binary phylogenetic trees the concept of maximum acyclic agreement forests is sufficient to com-pute hybridization networks with minimum hybridization number. In this work we demonstrate by, first, presenting an algorithm and, second, showing its cor-rectness that this concept is also sufficient in the case of multiple input trees. In detail, we show that for computing hybridization networks with minimum hy-bridization number for multiple rooted binary phylogenetic trees, it is sufficient to consider only maximum acyclic agreement forests instead of acyclic agreement forests of arbitrary size.