25,273 research outputs found
A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees
Reticulate events play an important role in determining evolutionary
relationships. The problem of computing the minimum number of such events to
explain discordance between two phylogenetic trees is a hard computational
problem. Even for binary trees, exact solvers struggle to solve instances with
reticulation number larger than 40-50. Here we present CycleKiller and
NonbinaryCycleKiller, the first methods to produce solutions verifiably close
to optimality for instances with hundreds or even thousands of reticulations.
Using simulations, we demonstrate that these algorithms run quickly for large
and difficult instances, producing solutions that are very close to optimality.
As a spin-off from our simulations we also present TerminusEst, which is the
fastest exact method currently available that can handle nonbinary trees: this
is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All
three methods are based on extensions of previous theoretical work and are
publicly available. We also apply our methods to real data
A quadratic kernel for computing the hybridization number of multiple trees
It has recently been shown that the NP-hard problem of calculating the
minimum number of hybridization events that is needed to explain a set of
rooted binary phylogenetic trees by means of a hybridization network is
fixed-parameter tractable if an instance of the problem consists of precisely
two such trees. In this paper, we show that this problem remains
fixed-parameter tractable for an arbitrarily large set of rooted binary
phylogenetic trees. In particular, we present a quadratic kernel
A first step towards computing all hybridization networks for two rooted binary phylogenetic trees
Recently, considerable effort has been put into developing fast algorithms to
reconstruct a rooted phylogenetic network that explains two rooted phylogenetic
trees and has a minimum number of hybridization vertices. With the standard
approach to tackle this problem being combinatorial, the reconstructed network
is rarely unique. From a biological point of view, it is therefore of
importance to not only compute one network, but all possible networks. In this
paper, we make a first step towards approaching this goal by presenting the
first algorithm---called allMAAFs---that calculates all
maximum-acyclic-agreement forests for two rooted binary phylogenetic trees on
the same set of taxa.Comment: 21 pages, 5 figure
Kernelizations for the hybridization number problem on multiple nonbinary trees
Given a finite set , a collection of rooted phylogenetic
trees on and an integer , the Hybridization Number problem asks if there
exists a phylogenetic network on that displays all trees from
and has reticulation number at most . We show two kernelization algorithms
for Hybridization Number, with kernel sizes and
respectively, with the number of input trees and their maximum
outdegree. Experiments on simulated data demonstrate the practical relevance of
these kernelization algorithms. In addition, we present an -time
algorithm, with and some computable function of
A simple fixed parameter tractable algorithm for computing the hybridization number of two (not necessarily binary) trees
Here we present a new fixed parameter tractable algorithm to compute the
hybridization number r of two rooted, not necessarily binary phylogenetic trees
on taxon set X in time (6^r.r!).poly(n)$, where n=|X|. The novelty of this
approach is its use of terminals, which are maximal elements of a natural
partial order on X, and several insights from the softwired clusters
literature. This yields a surprisingly simple and practical bounded-search
algorithm and offers an alternative perspective on the underlying combinatorial
structure of the hybridization number problem
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