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Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem

2010
*
IEEE/ACM Transactions on Computational Biology & Bioinformatics
*

Given a set L

doi:10.1109/tcbb.2008.93
pmid:20431153
fatcat:uswrhqdgafcxzfu5mgz55hnzue
*of*labels and a collection*of*rooted trees whose leaves are bijectively labelled by some elements*of*L,*the**Maximum**Agreement**Supertree**problem*(SMAST) is as follows: find a tree T on a largest ... In this paper, we focus on*the**parameterized*complexity*of*this NP-hard*problem*, considering different combinations*of**parameters*as well as particular cases. ... ACKNOWLEDGMENT This paper was supported by*the*Action incitative BIOSTIC-LR,*the*Action Jeunes Chercheurs*of*University Montpellier II and*the*french ANR PhylAriane. ...##
###
Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem

2010
*
IEEE/ACM Transactions on Computational Biology & Bioinformatics
*

Given a set L

doi:10.1109/tcbb.2010.30
fatcat:onpakczdn5fdffnc7gbg54okku
*of*labels and a collection*of*rooted trees whose leaves are bijectively labelled by some elements*of*L,*the**Maximum**Agreement**Supertree**problem*(SMAST) is as follows: find a tree T on a largest ... In this paper, we focus on*the**parameterized*complexity*of*this NP-hard*problem*, considering different combinations*of**parameters*as well as particular cases. ... ACKNOWLEDGMENT This paper was supported by*the*Action incitative BIOSTIC-LR,*the*Action Jeunes Chercheurs*of*University Montpellier II and*the*french ANR PhylAriane. ...##
###
Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem
[chapter]

*
Lecture Notes in Computer Science
*

Given a ground set L

doi:10.1007/978-3-540-73437-6_28
fatcat:3drtk3spyfbffmebrh2cxldree
*of*labels and a collection*of*trees whose leaves are bijectively labelled by some elements*of*L,*the**Maximum**Agreement**Supertree**problem*(SMAST) is*the*following: find a tree T on ...*The**problem*finds applications in phylogenetics, databases and data mining. In this paper we focus on*the**parameterized*complexity*of*this NP-hard*problem*. ...*The*SMAST*problem*consists in finding an*agreement**supertree*containing*the**maximum*number*of*labels from L. This*problem*is NP-hard in general as it generalizes*the*MAST*problem*[8] . ...##
###
Fixed-Parameter Algorithms in Phylogenetics
[chapter]

2008
*
Msphere
*

We survey

doi:10.1007/978-1-60327-159-2_24
pmid:18566780
fatcat:b7iiquxu5bcmxf776g4crrnepi
*the*use*of**fixed*-*parameter*algorithms in*the*field*of*phylogenetics, which is*the*study*of*evolutionary relationships. ...*The*numerous computational*problems*arising in phylogenetics often are NP-complete, but for many natural parametrizations they can be solved using*fixed*-*parameter*algorithms. ... For us, it is*of*particular interest that*MAXIMUM**AGREEMENT*SUBTREE is*fixed*-*parameter**tractable*with respect to*parameter*k (number*of*removed taxa): Sketch*of*proof ideas. ...##
###
Fixed-Parameter Algorithms in Phylogenetics

2007
*
Computer journal
*

We survey

doi:10.1093/comjnl/bxm049
fatcat:txfzhsnt3zebffedefjbfacwue
*the*use*of**fixed*-*parameter*algorithms in*the*field*of*phylogenetics, which is*the*study*of*evolutionary relationships. ...*The*numerous computational*problems*arising in phylogenetics often are NP-complete, but for many natural parametrizations they can be solved using*fixed*-*parameter*algorithms. ... For us, it is*of*particular interest that*MAXIMUM**AGREEMENT*SUBTREE is*fixed*-*parameter**tractable*with respect to*parameter*k (number*of*removed taxa): Sketch*of*proof ideas. ...##
###
Maximum agreement and compatible supertrees

2007
*
Journal of Discrete Algorithms
*

SMAST is shown to be W[2]-hard when

doi:10.1016/j.jda.2006.08.005
fatcat:z432pbbufrgxzgv2laq6yqqvv4
*the*considered*parameter*is*the*number*of*input leaves that have to be removed to obtain*the**agreement**of**the*input trees. A similar result holds for SMCT. ... In this paper, we propose extensions*of*these*problems*to*the*context*of**supertree*inference, where input trees have non-identical leaf sets. ... MAST and MCT are known to be*fixed*-*parameter**tractable*(FPT) in p,*the*smallest number*of*leaves to remove from*the*input set*of*leaves such that*the*input trees agree. ...##
###
Parameterized Algorithms in Bioinformatics: An Overview

2019
*
Algorithms
*

Aside from reporting

doi:10.3390/a12120256
fatcat:4dhjdnpibzh43iifgan2fu6bwa
*the*state*of**the*art, we give challenges and open*problems*for each topic. ... This work surveys recent developments*of**parameterized*algorithms and complexity for important NP-hard*problems*in bioinformatics. ... Finally, we thank*the*anonymous reviewers for their helpful and productive comments. Conflicts*of*Interest:*The*authors declare no conflict*of*interest. ...##
###
Maximum Agreement and Compatible Supertrees
[chapter]

2004
*
Lecture Notes in Computer Science
*

SMAST is shown to be W[2]-hard when

doi:10.1007/978-3-540-27801-6_15
fatcat:hchjnoadnber7feo45i55l3puu
*the*considered*parameter*is*the*number*of*input leaves that have to be removed to obtain*the**agreement**of**the*input trees. A simlar result holds for SMCT. ... In this paper, we propose extensions*of*these*problems*to*the*context*of**supertree*inference, where input trees have non-identical leaf sets. ... MAST and MCT are known to be*fixed*-*parameter**tractable*(FPT ) in p,*the*smallest number*of*leaves to remove from*the*input set*of*leaves such that*the*input trees agree. ...##
###
Towards a Data Reduction for the Minimum Flip Supertree Problem
[article]

2011
*
arXiv
*
pre-print

In computational phylogenetics,

arXiv:1104.4471v1
fatcat:kxjx5hmacrd2jksreoh3plccjq
*the**problem**of*constructing a*supertree**of*a given set*of*rooted input trees can be formalized in different ways, to cope with contradictory information in*the*input. ... We consider*the*Minimum Flip*Supertree**problem*, where*the*input trees are transformed into a 0/1/? ... Finding a kernel for*the*MFST*problem*, on*the*other hand, is related to*the*open question whether MFST is*parameterized**tractable*. I M (v) := {t : M [t, v] = 1} be*the*set*of*'1'-indices in column v. ...##
###
Improved Parameterized Complexity of the Maximum Agreement Subtree and Maximum Compatible Tree Problems

2006
*
IEEE/ACM Transactions on Computational Biology & Bioinformatics
*

Acknowledgement

doi:10.1109/tcbb.2006.39
pmid:17048466
fatcat:kgzvgwsosbdipam4vzx3wqkoma
*The*authors thank C. Paul and J. Cassaigne for careful readings*of**the*manuscript and help in simplifying some proofs. ...*The*authors are also grateful to anonymous reviewers for their valuable comments. ...*FIXED*-*PARAMETER**TRACTABILITY**OF*MAST AND MCT*FIXED*-*PARAMETER**TRACTABILITY**OF*MAST AND MCT ...##
###
Page 644 of Mathematical Reviews Vol. , Issue 2000a
[page]

2000
*
Mathematical Reviews
*

known as

*the**maximum**agreement*subtree (MAST)*problem*, is solvable in polynomial time. ... We also show that both*problems*are hard for*the**parameterized*complexity class W[1], where*the**parameter*is*the*number*of*in- put trees or sequences. ...##
###
Supertrees Based on the Subtree Prune-and-Regraft Distance

2014
*
Systematic Biology
*

Although calculating

doi:10.1093/sysbio/syu023
pmid:24695589
pmcid:PMC4055872
fatcat:althli3qp5ft3pkrd4725xdlja
*the*rooted SPR distance between a pair*of*trees is NP-hard, our new*maximum**agreement*forestbased methods can reconcile trees with hundreds*of*taxa and > 50 transfers in fractions ... We present*the*first method to construct*supertrees*by using*the*subtree prune-and-regraft (SPR) distance as an optimality criterion. ... ACKNOWLEDGMENTS We thank Joel Navarrete for his help in evaluating variants*of*our*supertree*approach. ...##
###
Advancing Divide-and-Conquer Phylogeny Estimation
[article]

2020
*
bioRxiv
*
pre-print

that is related to

doi:10.1101/2020.05.16.099895
fatcat:d4w7z2nxazczzjerwfahzcssbm
*maximum*likelihood*supertrees*), and we prove that finding*the*RFS*of*three input trees is NP-hard. ... However,*the*construction*of**the*Tree*of*Life is enormously computationally challenging, as all*the*current most accurate methods are either heuristics for NP-hard optimization*problems*or Bayesian MCMC ... Acknowledgments This research was supported by NSF grants 1458652, 1513629, and 1535977 to TW, by*the*NSF Graduate Research Fellowship DGE-1144245 to EKM, and by ...##
###
Constructing a Consensus Phylogeny from a Leaf-Removal Distance
[article]

2019
*
arXiv
*
pre-print

We also introduce a variant that minimizes

arXiv:1705.05295v3
fatcat:mavu7ycgunb4zh5vbbesrupo5i
*the**maximum*number d*of*leaves that are removed from any input tree, and provide a*parameterized*algorithm for this*problem*with*parameter*d. ... This*problem*is a specific instance*of**the*general consensus/*supertree**problem*, widely used to combine or summarize discordant evolutionary trees. ... Acknowledgement: MJ was partially supported by Labex NUMEV (ANR-10-LABX-20) and Vidi grant 639.072.602 from*The*Netherlands Organization for Scientific Research (NWO). ...##
###
SUPERTRIPLETS: a triplet-based supertree approach to phylogenomics

2010
*
Bioinformatics
*

A recurrent

doi:10.1093/bioinformatics/btq196
pmid:20529895
pmcid:PMC2881381
fatcat:73xg5pf2pfe5tjuwjwe2mnyphq
*problem*is to reconcile*the*various phylogenies built from different genomic sequences into a single one. ... This task is generally conducted by a two-step approach whereby a binary representation*of**the*initial trees is first inferred and then a*maximum*parsimony (MP) analysis is performed on it. ... ACKNOWLEDGEMENTS We thank*the*three referees for their suggestions on*the*manuscript. We also thank Guillaume Dugas for*the*SuperTriplets webpage and Khalid Belkhir for helpful advices. ...
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