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Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem

Sylvain Guillemot, Vincent Berry
2010 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
Given a set L 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.  ... 
doi:10.1109/tcbb.2008.93 pmid:20431153 fatcat:uswrhqdgafcxzfu5mgz55hnzue

Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem

Sylvain Guillemot, Vincent Berry
2010 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
Given a set L 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.  ... 
doi:10.1109/tcbb.2010.30 fatcat:onpakczdn5fdffnc7gbg54okku

Fixed-Parameter Tractability of the Maximum Agreement Supertree Problem [chapter]

Sylvain Guillemot, Vincent Berry
Lecture Notes in Computer Science  
Given a ground set L 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] .  ... 
doi:10.1007/978-3-540-73437-6_28 fatcat:3drtk3spyfbffmebrh2cxldree

Fixed-Parameter Algorithms in Phylogenetics [chapter]

Jens Gramm, Arfst Nickelsen, Till Tantau
2008 Msphere  
We survey 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.  ... 
doi:10.1007/978-1-60327-159-2_24 pmid:18566780 fatcat:b7iiquxu5bcmxf776g4crrnepi

Fixed-Parameter Algorithms in Phylogenetics

J. Gramm, A. Nickelsen, T. Tantau
2007 Computer journal  
We survey 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.  ... 
doi:10.1093/comjnl/bxm049 fatcat:txfzhsnt3zebffedefjbfacwue

Maximum agreement and compatible supertrees

Vincent Berry, François Nicolas
2007 Journal of Discrete Algorithms  
SMAST is shown to be W[2]-hard when 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.  ... 
doi:10.1016/j.jda.2006.08.005 fatcat:z432pbbufrgxzgv2laq6yqqvv4

Parameterized Algorithms in Bioinformatics: An Overview

Laurent Bulteau, Mathias Weller
2019 Algorithms  
Aside from reporting 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.  ... 
doi:10.3390/a12120256 fatcat:4dhjdnpibzh43iifgan2fu6bwa

Maximum Agreement and Compatible Supertrees [chapter]

Vincent Berry, François Nicolas
2004 Lecture Notes in Computer Science  
SMAST is shown to be W[2]-hard when 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.  ... 
doi:10.1007/978-3-540-27801-6_15 fatcat:hchjnoadnber7feo45i55l3puu

Towards a Data Reduction for the Minimum Flip Supertree Problem [article]

Sebastian Böcker
2011 arXiv   pre-print
In computational phylogenetics, 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.  ... 
arXiv:1104.4471v1 fatcat:kxjx5hmacrd2jksreoh3plccjq

Improved Parameterized Complexity of the Maximum Agreement Subtree and Maximum Compatible Tree Problems

V. Berry, F. Nicolas
2006 IEEE/ACM Transactions on Computational Biology & Bioinformatics  
Acknowledgement 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  ... 
doi:10.1109/tcbb.2006.39 pmid:17048466 fatcat:kgzvgwsosbdipam4vzx3wqkoma

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

Christopher Whidden, Norbert Zeh, Robert G. Beiko
2014 Systematic Biology  
Although calculating 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.  ... 
doi:10.1093/sysbio/syu023 pmid:24695589 pmcid:PMC4055872 fatcat:althli3qp5ft3pkrd4725xdlja

Advancing Divide-and-Conquer Phylogeny Estimation [article]

Xilin Yu, Thien Le, Sarah Christensen, Erin K Molloy, Tandy Warnow
2020 bioRxiv   pre-print
that is related to 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  ... 
doi:10.1101/2020.05.16.099895 fatcat:d4w7z2nxazczzjerwfahzcssbm

Constructing a Consensus Phylogeny from a Leaf-Removal Distance [article]

Cedric Chauve, Mark Jones, Manuel Lafond, Céline Scornavacca, Mathias Weller
2019 arXiv   pre-print
We also introduce a variant that minimizes 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).  ... 
arXiv:1705.05295v3 fatcat:mavu7ycgunb4zh5vbbesrupo5i

SUPERTRIPLETS: a triplet-based supertree approach to phylogenomics

V. Ranwez, A. Criscuolo, E. J. P. Douzery
2010 Bioinformatics  
A recurrent 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.  ... 
doi:10.1093/bioinformatics/btq196 pmid:20529895 pmcid:PMC2881381 fatcat:73xg5pf2pfe5tjuwjwe2mnyphq
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