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On the Compatibility of Quartet Trees

Noga Alon, Sagi Snir, Raphael Yuster
2014 SIAM Journal on Discrete Mathematics  
While every phylogenetic tree over n species defines n 4 quartets, not every set of quartets is compatible with some phylogenetic tree. Here we focus on the compatibility of quartet sets.  ...  On the other hand, in contrast to the classical result stating when Q is the densest, i.e. m = n 4 the consistency of any set of 3 quartets implies full consistency, we show that even for m = Θ( n 4 )  ...  Acknowledgments We tank the referees for their useful comments and for pointing to us the results of Colonius and Schulze [11] , the conjecture from Bendelt and Dress [2] and the result of Grünewald  ... 
doi:10.1137/130941043 fatcat:d2syriv4zzcyho4pn3er3fg4jq

On the compatibility of quartet trees [chapter]

Noga Alon, Sagi Snir, Raphael Yuster
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
While every phylogenetic tree over n species defines n 4 quartets, not every set of quartets is compatible with some phylogenetic tree. Here we focus on the compatibility of quartet sets.  ...  On the other hand, in contrast to the classical result stating when Q is the densest, i.e. m = n 4 the consistency of any set of 3 quartets implies full consistency, we show that even for m = Θ( n 4 )  ...  Acknowledgments We tank the referees for their useful comments and for pointing to us the results of Colonius and Schulze [11] , the conjecture from Bendelt and Dress [2] and the result of Grünewald  ... 
doi:10.1137/1.9781611973402.40 dblp:conf/soda/AlonSY14 fatcat:vmvccasfjbdx7lm2lncpeywgue

Improved Lower Bounds on the Compatibility of Multi-State Characters [article]

Brad Shutters, Sudheer Vakati, David Fernández-Baca
2012 arXiv   pre-print
We prove our result via a result on quartet compatibility that may be of independent interest: For every integer n > 4, there exists an incompatible set Q of n-2/2·n-2/2 + 1 quartets over n labels such  ...  We study a long standing conjecture on the necessary and sufficient conditions for the compatibility of multi-state characters: There exists a function f(r) such that, for any set C of r-state characters  ...  proper subset of Q s,t is compatible. ⊓ ⊔ The following theorem allows us to use our result on quartet compatibility to establish a lower bound on f (r).  ... 
arXiv:1205.5779v1 fatcat:4csmbnd3tnatdgqitmfm237lfm

Incompatible quartets, triplets, and characters

Brad Shutters, Sudheer Vakati, David Fernández-Baca
2013 Algorithms for Molecular Biology  
Our lower bound on f (r) is proven via a result on quartet compatibility that may be of independent interest: For every n ≥ 4, there exists an incompatible set Q of (n 2 ) quartets over n labels such that  ...  We study a long standing conjecture on the necessary and sufficient conditions for the compatibility of multi-state characters: There exists a function f (r) such that, for any set C of r-state characters  ...  This work was supported in part by the National Science Foundation under grants CCF-1017189 and DEB-0829674.  ... 
doi:10.1186/1748-7188-8-11 pmid:23547777 pmcid:PMC3694002 fatcat:l3txaj4yencmzohqxc74fj7ksu

Constructing Optimal Trees from Quartets

David Bryant, Mike Steel
2001 Journal of Algorithms  
We present fast new algorithms for constructing phylogenetic trees from quartets (resolved trees on four leaves).  ...  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  ...  Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the Canadian Genome Analysis and Technology grants to D. Sankoff.  ... 
doi:10.1006/jagm.2000.1133 fatcat:x3g3mnbb6vbapi3oui26entabu

The difficulty of constructing a leaf-labelled tree including or avoiding given subtrees

Meei Pyng Ng, Mike Steel, Nicholas C Wormald
2000 Discrete Applied Mathematics  
On the other hand, we show that the question of whether a fully resolved (binary) tree exists which has no subtree homeomorphic to one of the given ones is NP-complete, even when the given trees are rooted  ...  This sheds some light on the complexity of determining whether a probability assignment to trees is coherent.  ...  Acknowledgement The authors are grateful to the referees for their very helpful comments.  ... 
doi:10.1016/s0166-218x(99)00160-2 fatcat:zopcqqvpjncrbmejsxobpau7zi

Quartet-Net: A Quartet-Based Method to Reconstruct Phylogenetic Networks

Jialiang Yang, Stefan Grünewald, Xiu-Feng Wan
2013 Molecular biology and evolution  
Unlike distances that only reflect the relationship between a pair of taxa, quartets contain information on the relationships among four taxa; these quartets provide adequate capacity to infer a more accurate  ...  A software called "Quartet-Net" is implemented and available at  ...  This work was partially supported by the Natural Science Foundation of China (No. 10971213) to S.G., and Department of Justice (2010-DD-BX-0596) and National Institutes of Health (NIAID RC1AI086830) to  ... 
doi:10.1093/molbev/mst040 pmid:23493256 pmcid:PMC3670728 fatcat:l54md4iq7rh7zfxpgqgcnt4et4

Approximating the Complement of the Maximum Compatible Subset of Leaves of k Trees [chapter]

Ganeshkumar Ganapathy, Tandy Warnow
2002 Lecture Notes in Computer Science  
In this problem we are given a set of unrooted (not necessarily binary) trees each leaf-labelled by the same set ¤ , and we wish to remove a minimum number of leaves so that the resultant trees share a  ...  common refinement (i.e. they are "compatible").  ...  Acknowledgments This research was supported by a Fellowship in Science and Engineering from the David and Lucile Packard Foundation to Warnow, and by NSF grant EIA 01-21680 to Warnow.  ... 
doi:10.1007/3-540-45753-4_12 fatcat:5okd34t2ondr5ms6z3fwfklp2i

In VEST: Interactive and Visual Edge Selection Tool for Constructing Evolutionary Trees

Paul Kearney, Adrian Secord, Haoyong Zhang
1999 Biocomputing 2000  
InVEST allows the user to interact with and explore an ordered list of edges facilitating the incorporation of user domain knowledge into the evolutionary tree construction process. a The RDP's URL is  ...  In this paper it is shown that many methods for constructing evolutionary trees reduce to the edge selection problem.  ...  Acknowledgments The authors gratefully acknowledge the support of an NSERC undergraduate award, NSERC Research Grant 160321 and CITO.  ... 
doi:10.1142/9789814447331_0023 fatcat:xfpqcca6azhidcfbcd7mvizka4

Phylogenetic Closure Operations and Homoplasy-Free Evolution [chapter]

Tobias Dezulian, Mike Steel
2004 Classification, Clustering, and Data Mining Applications  
Q so that each quartet tree in the ordering introduces precisely one new leaf label, we say Q has a tight ordering for T.  ...  [C is "compatible", C "defines" T iff Q(C) does] 14 New quartet trees from old ones Example 1: qcl 2 Definition: If Q distinguishes every interior edge of a binary phylogenetic tree T and we can order  ...  Definition: For a binary phylogenetic tree T, a collection Q of displayed quartet trees is a generous cover for T if for all pairs u,v of interior vertices of T, we have a quartet xy|wz in Q that looks  ... 
doi:10.1007/978-3-642-17103-1_38 fatcat:ing3dczxdvh6fimhmedjg6nr7q

Computing Refined Buneman Trees in Cubic Time [chapter]

Gerth Stølting Brodal, Rolf Fagerberg, Anna Östlin, Christian N. S. Pedersen, S. Srinivasa Rao
2003 Lecture Notes in Computer Science  
The improved complexity of our algorithm makes the method of refined Buneman trees computational competitive to methods based on neighbor joining.  ...  Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics.  ...  The Buneman score of a quartet q = ab|cd, where a, b, c, d ∈ X is defined as: Compatibility A set of splits S is compatible if S ⊆ splits(T ) for some tree T . β q = 1 2 (min{ac + bd, ad + bc} − (ab +  ... 
doi:10.1007/978-3-540-39763-2_20 fatcat:xec4kitm2jbrdfdetwz34famca

Computing Refined Buneman Trees in Cubic Time

Gerth Stølting Brodal, Rolf Fagerberg, Anna Östlin, Christian N. S. Pedersen, S. Srinivasa Rao
2002 BRICS Report Series  
Reconstructing the evolutionary tree for a set of n species based on pairwise distances between the species is a fundamental problem in bioinformatics.  ...  Distance based methods based on the theory of Buneman trees and refined Buneman trees avoid this problem by only proposing evolutionary trees whose edges satisfy a number of constraints.  ...  Maintaining a set of compatible splits The running time of our algorithm for computing refined Buneman trees is dominanted by the maintenance of a set of compatible splits represented by an X-tree T .  ... 
doi:10.7146/brics.v9i51.21766 fatcat:r7kz3c33xbbynijdu2c3toxywu

Combinatorics of Linked Systems of Quartet Trees [article]

Emili Moan, Joseph Rusinko
2015 arXiv   pre-print
Moreover, we prove that this bound is optimal and give a lower-bound on the probability that a collection of quartets is decisive.  ...  We apply classical quartet techniques to the problem of phylogenetic decisiveness and find a value k such that all collections of at least k quartets are decisive.  ...  Mike Steel for introducing us to the concept of decisiveness and giving input throughout the writing process.  ... 
arXiv:1405.2464v2 fatcat:g5cxto7w6veffaxlp5hg4abcyq

Quartets in maximal weakly compatible split systems

S. Grünewald, J.H. Koolen, W.S. Lee
2009 Applied Mathematics Letters  
On the other hand, we construct maximal weakly compatible split systems where the number of induced quartets per quadruple tends to 0 with the number of taxa going to infinity.  ...  They are collections of bipartitions of a finite set X of taxa (e.g. species) with the property that, for every four taxa, at least one of the three bipartitions into two pairs (quartets) is not induced  ...  We denote the set of all quartets on X by Q(X). A subset of Q(X) is called a quartet system.  ... 
doi:10.1016/j.aml.2009.05.006 fatcat:x6ih3ueoiren3hm43quaphyiha

Faster reliable phylogenetic analysis

Vincent Berry, David Bryant
1999 Proceedings of the third annual international conference on Computational molecular biology - RECOMB '99  
We introduce and exploit combinatorial formalisms involving trees, quartets, and splits, and make particular use of an attractive duality between unrooted trees, splits, and dissimilarities on one hand  ...  , and rooted trees, clusters, and similarity measures on the other.  ...  Research supported in part by the Natural Sciences and Engineering Research Council of Canada and the Canadian Genome Analysis and Technology grants to D. Sankoff. V.  ... 
doi:10.1145/299432.299457 dblp:conf/recomb/BerryB99 fatcat:7a5gru22k5h7vnczr4ugx5mgpa
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