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

2007
*
IEEE/ACM Transactions on Computational Biology & Bioinformatics
*

However, in this paper, we show that

doi:10.1109/tcbb.2007.1019
pmid:17666765
fatcat:2z6ny3tyyzezxbxqajso2jly7i
*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. ...##
###
A quadratic kernel for computing the hybridization number of multiple trees
[article]

2012
*
arXiv
*
pre-print

network

arXiv:1203.4067v1
fatcat:np47omv2gzcyzm6bt3z6cx7a5u
*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 ...##
###
On the fixed parameter tractability of agreement-based phylogenetic distances

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*. ...

##
###
A quadratic kernel for computing the hybridization number of multiple trees

2013
*
Information Processing Letters
*

network

doi:10.1016/j.ipl.2013.02.010
fatcat:6zbeyd37tjec3hll23vlu5cobe
*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. ...##
###
Quantifying Hybridization in Realistic Time

2011
*
Journal of Computational Biology
*

In this paper, we give a new fixedparameter algorithm for

doi:10.1089/cmb.2009.0166
pmid:21210735
fatcat:tyzapa3brrhrtmfds4yyzalvdi
*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. ...##
###
Algorithms and Complexity in Phylogenetics (Dagstuhl Seminar 19443)

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*. ...

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

2013
*
Bulletin of Mathematical Biology
*

Furthermore, in an online appendix to

doi:10.1007/s11538-013-9874-x
pmid:23925727
fatcat:zo6tzgsij5ebreydq4oj7im2xu
*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 ...##
###
SPRIT: Identifying horizontal gene transfer in rooted phylogenetic trees

2010
*
BMC Evolutionary Biology
*

Identifying

doi:10.1186/1471-2148-10-42
pmid:20152048
pmcid:PMC2829038
fatcat:jiq5blcwqfbkzmtjw2wfjw4f44
*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. ...##
###
Phylogenetic incongruence through the lens of Monadic Second Order logic

2016
*
Journal of Graph Algorithms and Applications
*

Within

doi:10.7155/jgaa.00390
fatcat:ne7rpnylt5hhhlrz6acfk4c3sy
*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*. ...##
###
Phylogenetic incongruence through the lens of Monadic Second Order logic
[article]

2015
*
arXiv
*
pre-print

Within

arXiv:1503.00368v1
fatcat:ie42fw4m5nenrhjdmbeh56kqga
*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*. ...##
###
Cycle killer... qu'est-ce que c'est? On the comparative approximability of hybridization number and directed feedback vertex set
[article]

2011
*
arXiv
*
pre-print

We show that

arXiv:1112.5359v1
fatcat:n44w4ygrzzdnrpt32m5ae4frhu
*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. ...##
###
Drawing Tree-Based Phylogenetic Networks with Minimum Number of Crossings
[article]

2020
*
arXiv
*
pre-print

We show that, if reticulation edges are drawn x-monotone,

arXiv:2008.08960v1
fatcat:ttdfsa2ynrbzppqwhuac5scgs4
*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. ...##
###
Inferring Phylogenetic Networks Using PhyloNet
[article]

2017
*
bioRxiv
*
pre-print

As

doi:10.1101/238071
fatcat:zkz5ud35urdlliwku6lgshfv3u
*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*...##
###
Inferring Phylogenetic Networks Using PhyloNet

2018
*
Systematic Biology
*

As

doi:10.1093/sysbio/syy015
pmid:29514307
fatcat:k2xcf6kzwrg2nir7qtznhdmgpe
*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. ...##
###
A Reduction Algorithm for Computing the Hybridization Number of Two Trees

2007
*
Evolutionary Bioinformatics
*

Assuming that

doi:10.1177/117693430700300017
fatcat:3wioddmqxbdyviibqbbwaiqrdu
*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. ...
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