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On the Compatibility of Quartet Trees

2014
*
SIAM Journal on Discrete Mathematics
*

While every phylogenetic

doi:10.1137/130941043
fatcat:d2syriv4zzcyho4pn3er3fg4jq
*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 ...##
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On the compatibility of quartet trees
[chapter]

2013
*
Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms
*

While every phylogenetic

doi:10.1137/1.9781611973402.40
dblp:conf/soda/AlonSY14
fatcat:vmvccasfjbdx7lm2lncpeywgue
*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 ...##
###
Improved Lower Bounds on the Compatibility of Multi-State Characters
[article]

2012
*
arXiv
*
pre-print

We prove our result via a result

arXiv:1205.5779v1
fatcat:4csmbnd3tnatdgqitmfm237lfm
*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). ...##
###
Incompatible quartets, triplets, and characters

2013
*
Algorithms for Molecular Biology
*

Our lower bound

doi:10.1186/1748-7188-8-11
pmid:23547777
pmcid:PMC3694002
fatcat:l3txaj4yencmzohqxc74fj7ksu
*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. ...##
###
Constructing Optimal Trees from Quartets

2001
*
Journal of Algorithms
*

We present fast new algorithms for constructing phylogenetic

doi:10.1006/jagm.2000.1133
fatcat:x3g3mnbb6vbapi3oui26entabu
*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. ...##
###
The difficulty of constructing a leaf-labelled tree including or avoiding given subtrees

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. ...

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

2013
*
Molecular biology and evolution
*

Unlike distances that only reflect

doi:10.1093/molbev/mst040
pmid:23493256
pmcid:PMC3670728
fatcat:l54md4iq7rh7zfxpgqgcnt4et4
*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 ...##
###
Approximating the Complement of the Maximum Compatible Subset of Leaves of k Trees
[chapter]

2002
*
Lecture Notes in Computer Science
*

In this problem we are given a set

doi:10.1007/3-540-45753-4_12
fatcat:5okd34t2ondr5ms6z3fwfklp2i
*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. ...##
###
In VEST: Interactive and Visual Edge Selection Tool for Constructing Evolutionary Trees

1999
*
Biocomputing 2000
*

InVEST allows

doi:10.1142/9789814447331_0023
fatcat:xfpqcca6azhidcfbcd7mvizka4
*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. ...##
###
Phylogenetic Closure Operations and Homoplasy-Free Evolution
[chapter]

2004
*
Classification, Clustering, and Data Mining Applications
*

Q so that each

doi:10.1007/978-3-642-17103-1_38
fatcat:ing3dczxdvh6fimhmedjg6nr7q
*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 ...##
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Computing Refined Buneman Trees in Cubic Time
[chapter]

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 + ...

##
###
Computing Refined Buneman Trees in Cubic Time

2002
*
BRICS Report Series
*

Reconstructing

doi:10.7146/brics.v9i51.21766
fatcat:r7kz3c33xbbynijdu2c3toxywu
*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 . ...##
###
Combinatorics of Linked Systems of Quartet Trees
[article]

2015
*
arXiv
*
pre-print

Moreover, we prove that this bound is optimal and give a lower-bound

arXiv:1405.2464v2
fatcat:g5cxto7w6veffaxlp5hg4abcyq
*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. ...##
###
Quartets in maximal weakly compatible split systems

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. ...

##
###
Faster reliable phylogenetic analysis

1999
*
Proceedings of the third annual international conference on Computational molecular biology - RECOMB '99
*

We introduce and exploit combinatorial formalisms involving

doi:10.1145/299432.299457
dblp:conf/recomb/BerryB99
fatcat:7a5gru22k5h7vnczr4ugx5mgpa
*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. ...
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