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Computing Phylogenetic Roots with Bounded Degrees and Errors [chapter]

Zhi-Zhong Chen, Tao Jiang, Guo-Hui Lin
2001 Lecture Notes in Computer Science  
In this paper, we investigate PRk under a natural restriction that the maximum degree of the phylogenetic root is bounded from above by a constant.  ...  This is called the Phylogenetic kth Root Problem (PRk), and such a tree T , if exists, is called a phylogenetic kth root of graph G. The computational complexity of PRk is open, except for k ≤ 4.  ...  Acknowledgments GL would like to thank Paul Kearney for bringing CPRk to his attention, Bin Ma and Jinbo Xu for many helpful discussions.  ... 
doi:10.1007/3-540-44634-6_35 fatcat:djaascihurb4tjijvqlgvjkl64

Computing Phylogenetic Roots with Bounded Degrees and Errors

Zhi-Zhong Chen, Tao Jiang, Guohui Lin
2003 SIAM journal on computing (Print)  
In this paper, we investigate PRk under a natural restriction that the maximum degree of the phylogenetic root is bounded from above by a constant.  ...  This is called the Phylogenetic kth Root Problem (PRk), and such a tree T , if exists, is called a phylogenetic kth root of graph G. The computational complexity of PRk is open, except for k ≤ 4.  ...  Acknowledgments GL would like to thank Paul Kearney for bringing CPRk to his attention, Bin Ma and Jinbo Xu for many helpful discussions.  ... 
doi:10.1137/s0097539701389154 fatcat:ymds6cu22rd6zblxqz7ubu6tvm

Computing phylogenetic roots with bounded degrees and errors is NP-complete

Tatsuie Tsukiji, Zhi-Zhong Chen
2006 Theoretical Computer Science  
In the course of our proof, we will determine all trees (possibly with degree 2 nodes) that approximate the (s (k) − 1)-clique by errors at most 2.  ...  In this paper we study the computational complexity of the following optimization problem: given a graph G = (V , E), we wish to find a tree T such that (1) the degree of each internal node of T is at  ...  kth root T with at most errors.  ... 
doi:10.1016/j.tcs.2006.06.016 fatcat:5bga3s3wkvdxvetl6ifahwq7fe

Page 5074 of Mathematical Reviews Vol. , Issue 2004f [page]

2004 Mathematical Reviews  
roots with bounded degrees and errors.  ...  In this paper, the authors investigate PRA under a natural restriction that the maximum degree of the phylogenetic root is bounded from above by a constant.  ... 

Polytomies and Phylogenetically Independent Contrasts: Examination of the Bounded Degrees of Freedom Approach

Theodore Garland, Ramón Díaz-Uriarte, M. Westneat
1999 Systematic Biology  
We speci cally tested the adequacy of bounding degrees of freedom, as suggested by Purvis and Garland (1993; Syst. Biol. 42:569-575).  ...  Overall, and irrespective of evolutionary model, degrees of freedom were appropriately bounded for hypothesis testing, and unbiased estimates of the correlation coef cient were obtained.  ...  Bleiweiss and J. A. W. Kirsch for providing phylogenetic trees, C. Lázaro-Perea for comments on a previous version of the manuscript, and A.  ... 
doi:10.1080/106351599260139 pmid:12066293 fatcat:fca3ly2mw5ck5irc477xxeds6i

Constructing Optimal Trees from Quartets

David Bryant, Mike Steel
2001 Journal of Algorithms  
The main result is an algorithm for determining bounded degree trees with optimal quartet weight, subject to the constraint that the splits in the tree come from a given collection, for example, the splits  ...  The problem is central to divide and conquer approaches to phylogenetic analysis and has been receiving considerable attention from the computational biology community.  ...  Semple and V. Berry for help with proof reading.  ... 
doi:10.1006/jagm.2000.1133 fatcat:x3g3mnbb6vbapi3oui26entabu

Robinson-Foulds Reticulation Networks [article]

Alexey Markin, Tavis K Anderson, Venkata SKT Vadali, Oliver Eulenstein
2019 bioRxiv   pre-print
RF-Net was able to estimate a large and credible reassortment network with 164 taxa.  ...  Using simulations we experimentally validate the ability of our method, RF-Net, to reconstruct correct phylogenetic networks in the presence of error in input data.  ...  A (phylogenetic) network is a directed acyclic graph (DAG) with a designated root vertex of in-degree zero and all other vertices are either of in-degree one and out-degree two (tree vertices), in-degree  ... 
doi:10.1101/642793 fatcat:dtyox5djavfujlf3j3nucnbptu

Computing the maximum agreement of phylogenetic networks

Charles Choy, Jesper Jansson, Kunihiko Sadakane, Wing-Kin Sung
2005 Theoretical Computer Science  
with indegree 2.  ...  We prove that the problem is NPhard even if restricted to three phylogenetic networks and give an O(n 2 )-time algorithm for the special case of two level-1 phylogenetic networks, where n is the number  ...  Note that this is O(n log n) for two trees with maximum degree bounded by a constant and O(n 1.5 ) for two trees with unbounded degrees.  ... 
doi:10.1016/j.tcs.2004.12.012 fatcat:3r2u5fvqtzfbxig5y2dgclajeq

Computing the Maximum Agreement of Phylogenetic Networks

Charles Choy, Jesper Jansson, Kunihiko Sadakane, Wing-Kin Sung
2004 Electronical Notes in Theoretical Computer Science  
with indegree 2.  ...  We prove that the problem is NPhard even if restricted to three phylogenetic networks and give an O(n 2 )-time algorithm for the special case of two level-1 phylogenetic networks, where n is the number  ...  Note that this is O(n log n) for two trees with maximum degree bounded by a constant and O(n 1.5 ) for two trees with unbounded degrees.  ... 
doi:10.1016/j.entcs.2003.12.009 fatcat:4gmsoivhrvgz5kvsdysn4yjxdq

On the Inference of Large Phylogenies with Long Branches: How Long Is Too Long?

Elchanan Mossel, Sébastien Roch, Allan Sly
2010 Bulletin of Mathematical Biology  
The accurate reconstruction of phylogenies from short molecular sequences is an important problem in computational biology.  ...  Here, we consider a more general evolutionary model, the GTR model, where the q × q rate matrix Q is reversible with q ≥ 2. For this model, recent results of Roch E.  ...  the original author(s) and source are credited.  ... 
doi:10.1007/s11538-010-9584-6 pmid:20931293 fatcat:bfjxipzjnvhsxkr5zna2jvnjea

Evaluation of ultrametric phylogenetic tree estimation

Yujin Chung
2020 Journal of the Korean Data and Information Science Society  
The three parameterizations, called relAge, Thorne, and Rambaut, were found to be correctly estimated in most cases, although the relAge parameterization resulted in tree estimation with zero-length branches  ...  A phylogenetic tree is a tree-like graphical representation of the evolutionary history of a group of organisms.  ...  The bound on the root-age can also be enforced by log transformation.  ... 
doi:10.7465/jkdi.2020.31.3.663 fatcat:3hfxp4fabvfyzc4n5s2pru474q

On the inference of large phylogenies with long branches: How long is too long? [article]

Elchanan Mossel and Sebastien Roch and Allan Sly
2010 arXiv   pre-print
Here, we show that this phenomenon also holds for phylogenetic reconstruction by exhibiting a family of symmetric models Q and a phylogenetic reconstruction algorithm which recovers the tree from O( n)  ...  For this model, recent results of [Roch'09] show that the tree can be accurately reconstructed with sequences of length O((n)) when the branch lengths are below , known as the Kesten-Stigum (KS) bound.  ...  Proposition 1 shows that this "error channel" is of the Potts type with bounded length, no matter how deep the tree.  ... 
arXiv:1001.3480v1 fatcat:5wklttmz6zgdfkx53azn2fvfjq

A reduction algorithm for computing the hybridization number of two trees

Magnus Bordewich, Simone Linz, Katherine St John, Charles Semple
2007 Evolutionary Bioinformatics  
Although the two-tree problem is NP-hard, our algorithm always gives the exact solution and runs efficiently on many real biological problems.  ...  Previous algorithms for the two-tree problem either solve a restricted version of the problem or give an answer with no guarantee of the closeness to the exact solution.  ...  Acknowledgment The authors thank Heiko Schmidt for providing them with the reconstructed gene trees of the grass data set.  ... 
pmid:19461978 pmcid:PMC2684132 fatcat:kuqoq7l2hjespphfc2iv3jshz4

Fast and accurate inference of phylogenetic networks using large-scale genomic sequence data [article]

Hussein Hejase, Natalie VandePol, Gregory M Bonito, Kevin J Liu
2017 bioRxiv   pre-print
The answer to this fundamental question not only depends upon densely sampled and divergent genomic sequence data, but also computational methods which are capable of accurately and efficiently inferring  ...  We conduct a performance study involving a range of evolutionary scenarios, and we demonstrate that FastNet outperforms state-of-the-art methods in terms of computational efficiency and topological accuracy  ...  CCF-1565719 (to KJL), CCF-1714417 (to KJL), and DEB-1737898 (to GMB and KJL), BEACON grants (NSF STC Cooperative Agreement DBI-093954) to GMB and KJL, and computing resources provided by MSU HPCC.  ... 
doi:10.1101/132795 fatcat:zhagnarpv5agrbhvvbfopzdhja

Comparison of Tree-Child Phylogenetic Networks [article]

Gabriel Cardona, Francesc Rossello, Gabriel Valiente
2007 arXiv   pre-print
Simple, polynomial algorithms for reconstructing a tree-child phylogenetic network from its path multiplicity vectors, for computing the distance between two tree-child phylogenetic networks, and for aligning  ...  a pair of tree-child phylogenetic networks, are provided, and they have been implemented as a Perl package and a Java applet, and they are available at http://bioinfo.uib.es/~recerca/phylonetworks/mudistance  ...  -C02-01, and by EU project INTAS IT 04-77-7178.  ... 
arXiv:0708.3499v1 fatcat:w7n77mmgznds5gicayk3pmz3m4
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