Hybridization in Nonbinary Trees

Linz, Simone; Semple, Charles

doi:10.1109/tcbb.2008.86

Cited by 25 publications

(39 citation statements)

References 12 publications

(8 reference statements)

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“…Another question is whether the kernel size can be reduced for certain fixed |T |. For |T | = 2, our results give a cubic kernel, while Linz and Semple [20] showed a linear kernel of a modified, weighted problem, by analyzing carefully how common chains can look in two trees. Can something like this be done for more than two trees?…”

Section: Discussion and Open Problemsmentioning

confidence: 82%

“…For the case of two nonbinary trees, there is also a polynomial kernel [20], based on a highly technical kernelization argument, and a simpler FPT algorithm based on bounded search [25].…”

Section: Introductionmentioning

confidence: 99%

“…This helps us to avoid a technical case analysis (as in [20]) and exhaustive guessing (as in [18]), leading to a simple and unified kernelization approach that is applicable to a more general problem (compared to e.g. [20,15]).…”

Section: Introductionmentioning

confidence: 99%

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Kernelizations for the hybridization number problem on multiple nonbinary trees

Iersel

Kelk

Scornavacca

2016

Journal of Computer and System Sciences

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Given a finite set X, a collection T of rooted phylogenetic trees on X and an integer k, the Hybridization Number problem asks if there exists a phylogenetic network on X that displays all trees from T and has reticulation number at most k. We show two kernelization algorithms for Hybridization Number, with kernel sizes 4k(5k) t and 20k 2 ( + − 1) respectively, with t the number of input trees and + their maximum outdegree. Experiments on simulated data demonstrate the practical relevance of our kernelization algorithms. In addition, we present an n f (k) t-time algorithm, with n = |X| and f some computable function of k.

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Section: Discussion and Open Problemsmentioning

confidence: 82%

“…For the case of two nonbinary trees, there is also a polynomial kernel [20], based on a highly technical kernelization argument, and a simpler FPT algorithm based on bounded search [25].…”

Section: Introductionmentioning

confidence: 99%

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Kernelizations for the hybridization number problem on multiple nonbinary trees

Iersel

Kelk

Scornavacca

2016

Journal of Computer and System Sciences

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“…A recent result by Linz and Semple [22] shows that computing the hybridization number of two rooted multifurcating trees is fixed-parameter tractable. However, the parameterized complexity of the Max-AF problem on multifurcating trees remained unknown.…”

Section: Introductionmentioning

confidence: 99%

A fixed-parameter algorithm for the maximum agreement forest problem on multifurcating trees

Shi

Wang

Yang

et al. 2015

Sci. China Inf. Sci.

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The Maximum Agreement Forest (MAF) problem on two given phylogenetic trees is an important NP-hard problem in the field of computational biology. In this paper, we study the parameterized version of the MAF problem: given two unrooted (multifurcating) phylogenetic trees T 1 and T 2 with the same leaf-label set L, and a parameter k, either construct an agreement forest of at most k trees for T 1 and T 2 , or report that no such a forest exists. Whether there is a fixed-parameter tractable algorithm for this problem was posed as an open problem several times in the literature. In this paper, we resolve this open problem by presenting a parameterized algorithm of running time O(4 k n 5 ) for the problem.

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“…There are several existing approaches for reconstructing the exact minimum reticulate networks when there are only two gene trees (Bordewich et al , 2007; Linz and Semple, 2009; Wu, 2009; Wu and Wang, 2010). Clearly restricting to just two gene trees is a big limitation: more gene trees will be more informative to phylogenetic inference, and DNA sequences of many genes are available.…”

Section: Introductionmentioning

confidence: 99%

Close lower and upper bounds for the minimum reticulate network of multiple phylogenetic trees

2010

Bioinformatics

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Motivation: Reticulate network is a model for displaying and quantifying the effects of complex reticulate processes on the evolutionary history of species undergoing reticulate evolution. A central computational problem on reticulate networks is: given a set of phylogenetic trees (each for some region of the genomes), reconstruct the most parsimonious reticulate network (called the minimum reticulate network) that combines the topological information contained in the given trees. This problem is well-known to be NP-hard. Thus, existing approaches for this problem either work with only two input trees or make simplifying topological assumptions.Results: We present novel results on the minimum reticulate network problem. Unlike existing approaches, we address the fully general problem: there is no restriction on the number of trees that are input, and there is no restriction on the form of the allowed reticulate network. We present lower and upper bounds on the minimum number of reticulation events in the minimum reticulate network (and infer an approximately parsimonious reticulate network). A program called PIRN implements these methods, which also outputs a graphical representation of the inferred network. Empirical results on simulated and biological data show that our methods are practical for a wide range of data. More importantly, the lower and upper bounds match for many datasets (especially when the number of trees is small or reticulation level is low), and this allows us to solve the minimum reticulate network problem exactly for these datasets.Availability: A software tool, PIRN, is available for download from the web page: http://www.engr.uconn.edu/~ywu.Contact: ywu@engr.uconn.eduSupplementary information: Supplementary data is available at Bioinformatics online.

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Hybridization in Nonbinary Trees

Cited by 25 publications

References 12 publications

Kernelizations for the hybridization number problem on multiple nonbinary trees

Kernelizations for the hybridization number problem on multiple nonbinary trees

A fixed-parameter algorithm for the maximum agreement forest problem on multifurcating trees

Close lower and upper bounds for the minimum reticulate network of multiple phylogenetic trees

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