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Computing the Hybridization Number of Two Phylogenetic Trees Is Fixed-Parameter Tractable

M. Bordewich, C. Semple
2007 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
However, in this paper, we show that the problem is fixed-parameter tractable in the two-tree instance, when parameterized by this smallest number of reticulation vertices.  ...  It has been previously shown that this problem is NP-hard even when the collection consists of only two rooted binary phylogenetic trees.  ...  This satisfies the conditions for Hybridization Number to be fixed-parameter tractable. 2 Remark.  ... 
doi:10.1109/tcbb.2007.1019 pmid:17666765 fatcat:2z6ny3tyyzezxbxqajso2jly7i

A quadratic kernel for computing the hybridization number of multiple trees [article]

Leo van Iersel, Simone Linz
2012 arXiv   pre-print
network is fixed-parameter tractable if an instance of the problem consists of precisely two such 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  ...  Leo van Iersel was funded by a Veni grant of The Netherlands Organization for Scientific Research (NWO) and Simone Linz by the University of Tübingen and a travel fellowship by the German Academic Exchange  ... 
arXiv:1203.4067v1 fatcat:np47omv2gzcyzm6bt3z6cx7a5u

On the fixed parameter tractability of agreement-based phylogenetic distances

Magnus Bordewich, Celine Scornavacca, Nihan Tokac, Mathias Weller
2016 Journal of Mathematical Biology  
The respective problems of computing these measures are known to be NP-hard, but also fixed-parameter tractable in their respective natural parameters.  ...  Bordewich et al. one, where n is the number of leaves of the phylogenetic trees, p is the natural parameter and k is a much stronger (that is, smaller) parameter: the minimum level of a phylogenetic network  ...  Part of the work has been conceived at the 7th workshop on Graph Classes, Optimization, and Width Parameters.  ... 
doi:10.1007/s00285-016-1023-3 pmid:27221239 fatcat:5rocei5ibvgdxao3ptdnpau4qm

A quadratic kernel for computing the hybridization number of multiple trees

Leo van Iersel, Simone Linz
2013 Information Processing Letters  
network is fixed-parameter tractable if an instance of the problem consists of precisely two such 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  ...  We thank Steven Kelk and Charles Semple for many helpful discussions on the topic of this paper, and two anonymous reviewers for their comments.  ... 
doi:10.1016/j.ipl.2013.02.010 fatcat:6zbeyd37tjec3hll23vlu5cobe

Quantifying Hybridization in Realistic Time

Joshua Collins, Simone Linz, Charles Semple
2011 Journal of Computational Biology  
In this paper, we give a new fixedparameter algorithm for computing the minimum number of hybridization events for when two rooted binary phylogenetic trees are given.  ...  It has been shown that inferring the minimum number of hybridization events that is needed to simultaneously explain the evolutionary history for a set of trees is an NP-hard and also fixedparameter tractable  ...  Mathematically speaking, a problem of size n, parameterized by k, is fixed-parameter tractable if it can be computed in O(f (k)p(n)), where f is a computable function and p is a fixed polynomial.  ... 
doi:10.1089/cmb.2009.0166 pmid:21210735 fatcat:tyzapa3brrhrtmfds4yyzalvdi

Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)

Magnus Bordewich, Britta Dorn, Simone Linz, Rolf Niedermeier, Michael Wagner
2020 Dagstuhl Reports  
Phylogenetics is the study of ancestral relationships between species. Its central goal is the reconstruction and analysis of phylogenetic trees and networks.  ...  Even though research in phylogenetics is motivated by biological questions and applications, it heavily relies on mathematics and computer science.  ...  Our working group proved that the hybridization number problem is fixed-parameter tractable in both of these parameterizations.  ... 
doi:10.4230/dagrep.9.10.134 dblp:journals/dagstuhl-reports/BordewichDLN19 fatcat:nypkd3nzjvg5jdsd3cidktwyei

Cherry Picking: A Characterization of the Temporal Hybridization Number for a Set of Phylogenies

Peter J. Humphries, Simone Linz, Charles Semple
2013 Bulletin of Mathematical Biology  
Furthermore, in an online appendix to the paper, we show that this new characterization can be used to show that computing the minimumtemporal hybridization number for two trees is fixed-parameter tractable  ...  Recently, we have shown that calculating the minimum-temporal-hybridization number for a set P of rooted binary phylogenetic trees is NP-hard and have characterized this minimum number when P consists  ...  Acknowledgements We thank the referees for their helpful comments. References  ... 
doi:10.1007/s11538-013-9874-x pmid:23925727 fatcat:zo6tzgsij5ebreydq4oj7im2xu

SPRIT: Identifying horizontal gene transfer in rooted phylogenetic trees

Tobias Hill, Karl JV Nordström, Mikael Thollesson, Tommy M Säfström, Andreas KE Vernersson, Robert Fredriksson, Helgi B Schiöth
2010 BMC Evolutionary Biology  
Identifying the minimum number of RSPRs separating two trees is NP-hard, but the problem can be reduced to fixed parameter tractable.  ...  Results: We present the SPR Identification Tool (SPRIT), a novel algorithm that solves the fixed parameter tractable minimum RSPR problem and its GPL licensed Java implementation.  ...  the studies.  ... 
doi:10.1186/1471-2148-10-42 pmid:20152048 pmcid:PMC2829038 fatcat:jiq5blcwqfbkzmtjw2wfjw4f44

Phylogenetic incongruence through the lens of Monadic Second Order logic

Steven Kelk, Leo van Iersel, Celine Scornavacca, Mathias Weller
2016 Journal of Graph Algorithms and Applications  
Within the field of phylogenetics there is growing interest in measures for summarising the dissimilarity, or incongruence, of two or more phylogenetic trees.  ...  Many of these measures are NP-hard to compute and this has stimulated a considerable volume of research into fixed parameter tractable algorithms.  ...  On the positive side, however, the phylogenetics community has been quite successful in proving that these measures are fixed parameter tractable (FPT) in their natural parameterizations.  ... 
doi:10.7155/jgaa.00390 fatcat:ne7rpnylt5hhhlrz6acfk4c3sy

Phylogenetic incongruence through the lens of Monadic Second Order logic [article]

Steven Kelk, Leo van Iersel, Celine Scornavacca
2015 arXiv   pre-print
Within the field of phylogenetics there is growing interest in measures for summarising the dissimilarity, or 'incongruence', of two or more phylogenetic trees.  ...  Many of these measures are NP-hard to compute and this has stimulated a considerable volume of research into fixed parameter tractable algorithms.  ...  On the positive side, however, the phylogenetics community has been quite successful in proving that these measures are fixed parameter tractable (FPT) in their natural parameterizations.  ... 
arXiv:1503.00368v1 fatcat:ie42fw4m5nenrhjdmbeh56kqga

Cycle killer... qu'est-ce que c'est? On the comparative approximability of hybridization number and directed feedback vertex set [article]

Steven Kelk, Leo van Iersel, Nela Lekic, Simone Linz, Celine Scornavacca, Leen Stougie
2011 arXiv   pre-print
We show that the problem of computing the hybridization number of two rooted binary phylogenetic trees on the same set of taxa X has a constant factor polynomial-time approximation if and only if the problem  ...  On the positive side, we use results from the DFVS literature to give an O(log r log log r) approximation for hybridization number, where r is the value of an optimal solution to the hybridization number  ...  Then The fixed parameter tractability of MinimumHybridization now follows from the next lemma, which bounds the number of leaves in a reduced tree pair.  ... 
arXiv:1112.5359v1 fatcat:n44w4ygrzzdnrpt32m5ae4frhu

Drawing Tree-Based Phylogenetic Networks with Minimum Number of Crossings [article]

Jonathan Klawitter, Peter Stumpf
2020 arXiv   pre-print
We show that, if reticulation edges are drawn x-monotone, the problem is NP-complete, but fixed-parameter tractable in the number of reticulation edges.  ...  One aesthetic criteria is to minimize the number of crossings between tree edges and reticulation edges. This optimization problem has not yet been researched.  ...  Then a snake-style drawing of N with minimum number of crossings can be computed in O(2 k ·nk) time. The computation is thus fixed-parameter tractable when parametrized by k. Proof.  ... 
arXiv:2008.08960v1 fatcat:ttdfsa2ynrbzppqwhuac5scgs4

Inferring Phylogenetic Networks Using PhyloNet [article]

Dingqiao Wen, Yun Yun, Jiafan Zhu, Luay Nakhleh
2017 bioRxiv   pre-print
As computing the likelihood of a phylogenetic network is computationally hard, PhyloNet allows for evaluation and inference of networks using a pseudo-likelihood measure.  ...  The software package now includes a wide array of methods for inferring phylogenetic networks from data sets of unlinked loci while accounting for both reticulation (e.g., hybridization) and incomplete  ...  A phylogenetic network extends the phylogenetic tree (a) A phylogenetic network on fix taxa, with taxon D missing (due to extinction or incomplete sampling), and a hybridization involving (ancestors of  ... 
doi:10.1101/238071 fatcat:zkz5ud35urdlliwku6lgshfv3u

Inferring Phylogenetic Networks Using PhyloNet

Dingqiao Wen, Yun Yu, Jiafan Zhu, Luay Nakhleh, David Posada
2018 Systematic Biology  
As computing the likelihood of a phylogenetic network is computationally hard, PhyloNet allows for evaluation and inference of networks using a pseudolikelihood measure.  ...  The software package now includes a wide array of methods for inferring phylogenetic networks from data sets of unlinked loci while accounting for both reticulation (e.g., hybridization) and incomplete  ...  ACKNOWLEDGMENTS We would like to thank the PhyloNet users for submitting bug reports, feature requests, and other comments that helped us significantly improve the software.  ... 
doi:10.1093/sysbio/syy015 pmid:29514307 fatcat:k2xcf6kzwrg2nir7qtznhdmgpe

A Reduction Algorithm for Computing the Hybridization Number of Two Trees

Magnus Bordewich, Simone Linz, Katherine St. John, Charles Semple
2007 Evolutionary Bioinformatics  
Assuming that the initial set of gene trees is correct, a basic problem for biologists is to compute the minimum number of hybridization events to explain this set.  ...  In this paper, we describe a new reduction-based algorithm for computing this minimum number for when the initial data set consists of two trees.  ...  Acknowledgment We thank Heiko Schmidt for providing us with the reconstructed gene trees of the grass data set.  ... 
doi:10.1177/117693430700300017 fatcat:3wioddmqxbdyviibqbbwaiqrdu
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