5,330 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
When two trees go to war
Rooted phylogenetic networks are often constructed by combining trees,
clusters, triplets or characters into a single network that in some
well-defined sense simultaneously represents them all. We review these four
models and investigate how they are related. In general, the model chosen
influences the minimum number of reticulation events required. However, when
one obtains the input data from two binary trees, we show that the minimum
number of reticulations is independent of the model. The number of
reticulations necessary to represent the trees, triplets, clusters (in the
softwired sense) and characters (with unrestricted multiple crossover
recombination) are all equal. Furthermore, we show that these results also hold
when not the number of reticulations but the level of the constructed network
is minimised. We use these unification results to settle several complexity
questions that have been open in the field for some time. We also give explicit
examples to show that already for data obtained from three binary trees the
models begin to diverge
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 hybrid swarm-based algorithm for single-objective optimization problems involving high-cost analyses
In many technical fields, single-objective optimization procedures in
continuous domains involve expensive numerical simulations. In this context, an
improvement of the Artificial Bee Colony (ABC) algorithm, called the Artificial
super-Bee enhanced Colony (AsBeC), is presented. AsBeC is designed to provide
fast convergence speed, high solution accuracy and robust performance over a
wide range of problems. It implements enhancements of the ABC structure and
hybridizations with interpolation strategies. The latter are inspired by the
quadratic trust region approach for local investigation and by an efficient
global optimizer for separable problems. Each modification and their combined
effects are studied with appropriate metrics on a numerical benchmark, which is
also used for comparing AsBeC with some effective ABC variants and other
derivative-free algorithms. In addition, the presented algorithm is validated
on two recent benchmarks adopted for competitions in international conferences.
Results show remarkable competitiveness and robustness for AsBeC.Comment: 19 pages, 4 figures, Springer Swarm Intelligenc
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