A Simple Fixed Parameter Tractable Algorithm for Computing the Hybridization Number of Two (Not Necessarily Binary) Trees
Here, we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set X in time (6 r r!) · poly(n), where n = |X|. The novelty of this approach is its use of terminals, which are maximal elements of a na...
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| Published in: | IEEE/ACM transactions on computational biology and bioinformatics Vol. 10; no. 1; pp. 18 - 25 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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United States
IEEE
01.01.2013
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1545-5963, 1557-9964, 1557-9964 |
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| Abstract | Here, we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set X in time (6 r r!) · poly(n), where n = |X|. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on X, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem. |
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| AbstractList | Here, we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set Χ in time (6(r)r!) · poly(n), where n = |Χ|. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on Χ, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem. Here, we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set X in time (6 r r!) · poly(n), where n = |X|. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on X, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem. Here, we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set Χ in time (6(r)r!) · poly(n), where n = |Χ|. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on Χ, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem.Here, we present a new fixed parameter tractable algorithm to compute the hybridization number r of two rooted, not necessarily binary phylogenetic trees on taxon set Χ in time (6(r)r!) · poly(n), where n = |Χ|. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on Χ, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem. Here, we present a new fixed parameter tractable algorithm to compute the hybridization number $(r)$ of two rooted, not necessarily binary phylogenetic trees on taxon set $({{\cal X}})$ in time $((6 rho r!) \cdot poly(n))$, where $(n=\vert {{\cal X}}\vert)$. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on $({{\cal X}})$, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem. Here, we present a new fixed parameter tractable algorithm to compute the hybridization number $(r)$ of two rooted, not necessarily binary phylogenetic trees on taxon set $({{\cal X}})$ in time $((6^r r!) \cdot poly(n))$, where $(n=\vert {{\cal X}}\vert)$. The novelty of this approach is its use of terminals, which are maximal elements of a natural partial order on $({{\cal X}})$, and several insights from the softwired clusters literature. This yields a surprisingly simple and practical bounded-search algorithm and offers an alternative perspective on the underlying combinatorial structure of the hybridization number problem. |
| Author | Piovesan, Teresa Kelk, Steven M. |
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| References | ref13 ref12 ref15 ref14 kelk (ref17) 0 whidden (ref29) 2012 ref2 (ref10) 2007 ref1 huson (ref11) 2012 ref19 nakhleh (ref22) 2009 ref18 semple (ref23) 2007 semple (ref24) 2003 ref26 ref20 flum (ref8) 2006 bordewich (ref4) 2007; 3 van iersel (ref25) 2012 ref28 ref27 kelk (ref16) 2012 morrison (ref21) 2011 ref7 (ref9) 2005 ref3 ref6 ref5 |
| References_xml | – ident: ref15 doi: 10.1093/sysbio/sys062 – year: 2012 ident: ref11 article-title: Computing Minimum Hybridization Networks from Real Phylogenetic Trees – ident: ref13 doi: 10.1017/CBO9780511974076 – year: 2005 ident: ref9 publication-title: Math of Evolution and Phylogeny – ident: ref26 doi: 10.1016/j.jtbi.2010.10.032 – ident: ref18 doi: 10.1109/TCBB.2011.128 – ident: ref6 doi: 10.1093/bioinformatics/btq548 – ident: ref7 doi: 10.1089/cmb.2009.0166 – ident: ref5 doi: 10.1016/j.dam.2006.08.008 – year: 2003 ident: ref24 publication-title: Phylogenetics doi: 10.1093/oso/9780198509424.001.0001 – year: 2007 ident: ref23 article-title: Hybridization Networks publication-title: Reconstructing Evolution - New Mathematical and Computational Advances – year: 2006 ident: ref8 publication-title: Parameterized Complexity Theory – year: 0 ident: ref17 article-title: Towards the Fixed Parameter Tractability of Constructing Minimal Phylogenetic Networks from Arbitrary Sets of Nonbinary Trees – ident: ref27 doi: 10.1093/bioinformatics/btq202 – ident: ref12 doi: 10.1093/bioinformatics/btp217 – year: 2012 ident: ref16 article-title: Constructing Minimal Phylogenetic Networks from Softwired Clusters Is Fixed Parameter Tractable publication-title: Algorithmica – ident: ref14 doi: 10.1093/gbe/evq077 – year: 2012 ident: ref29 article-title: Fixed-Parameter and Approximation Algorithms for Maximum Agreement Forests – ident: ref3 doi: 10.1007/s00026-004-0228-0 – year: 2007 ident: ref10 publication-title: Reconstructing Evolution New Mathematical and Computational Advances – ident: ref19 doi: 10.1137/120864350 – ident: ref28 doi: 10.1016/j.ipl.2013.02.010 – volume: 3 start-page: 86 year: 2007 ident: ref4 article-title: A Reduction Algorithm for Computing the Hybridization Number of Two Trees publication-title: Evolutionary Bioinformatics doi: 10.1177/117693430700300017 – ident: ref1 doi: 10.1093/bioinformatics/btr618 – ident: ref2 doi: 10.1007/s00285-005-0315-9 – ident: ref20 doi: 10.1109/TCBB.2008.86 – year: 2009 ident: ref22 article-title: Evolutionary Phylogenetic Networks: Models and Issues publication-title: The Problem Solving Handbook for Computational Biology and Bioinformatics – year: 2011 ident: ref21 publication-title: An Introduction to Phylogenetic Networks – year: 2012 ident: ref25 article-title: New Version of Phylogenetic Network Software |
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| SubjectTerms | Algorithms Bioinformatics Cluster Analysis Clustering algorithms Computational biology Computational Biology - methods fixed parameter tractability Hybridization, Genetic nonbinary Phylogenetic network Phylogeny Polynomials Silicon Vegetation |
| Title | A Simple Fixed Parameter Tractable Algorithm for Computing the Hybridization Number of Two (Not Necessarily Binary) Trees |
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