Reconstructing Phylogenetic Level-1 Networks from Nondense Binet and Trinet Sets

Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxon set X , and constructing such a network whenever it...

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Veröffentlicht in:	Algorithmica Jg. 77; H. 1; S. 173 - 200
Hauptverfasser:	Huber, Katharina T., van Iersel, Leo, Moulton, Vincent, Scornavacca, Celine, Wu, Taoyang
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.01.2017 Springer Nature B.V Springer Verlag
Schlagworte:	Algorithm Analysis and Problem Complexity Algorithms Bioinformatics Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Networks Phylogenetics Polynomials Theory of Computation Phylogenetic network NP-hard Supernetwork Phylogenetic tree Exponential-time algorithm Polynomial-time algorithm Trinet Aho algorithm
ISSN:	0178-4617, 1432-0541
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Abstract	Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxon set X , and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an O ( 3 \| X \| p o l y ( \| X \| ) ) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted phylogenetic networks.
AbstractList	Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxon set X , and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an O ( 3 \| X \| p o l y ( \| X \| ) ) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted phylogenetic networks. Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxon set X , and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an O(3 \|X \| poly(\|X \|)) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted phylogenetic networks. B Leo van Iersel Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxon set X, and constructing such a network whenever it exists. We show that this is NP-hard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an O ( 3 \| X \| p o l y ( \| X \| ) ) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted phylogenetic networks.
Author	Huber, Katharina T. Wu, Taoyang Moulton, Vincent van Iersel, Leo Scornavacca, Celine
Author_xml	– sequence: 1 givenname: Katharina T. surname: Huber fullname: Huber, Katharina T. organization: School of Computing Sciences, University of East Anglia – sequence: 2 givenname: Leo surname: van Iersel fullname: van Iersel, Leo email: l.j.j.v.iersel@gmail.com organization: Delft Institute of Applied Mathematics, Delft University of Technology – sequence: 3 givenname: Vincent surname: Moulton fullname: Moulton, Vincent organization: School of Computing Sciences, University of East Anglia – sequence: 4 givenname: Celine surname: Scornavacca fullname: Scornavacca, Celine organization: ISEM, CNRS – Université Montpellier, Institut de Biologie Computationnelle – sequence: 5 givenname: Taoyang surname: Wu fullname: Wu, Taoyang organization: School of Computing Sciences, University of East Anglia
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Cites_doi	10.1371/journal.pcbi.1004135 10.1109/TCBB.2008.70 10.1093/oxfordjournals.molbev.a025664 10.1371/journal.pone.0106531 10.1137/S0097539704446529 10.1073/pnas.1407950111 10.1109/TCBB.2004.44 10.1016/j.tig.2013.05.007 10.1109/TCBB.2010.17 10.1080/10635150601167013 10.1137/0210030 10.1093/sysbio/syu076 10.1142/S0219720004000521 10.1007/s00453-012-9659-x 10.1016/j.jda.2013.10.002 10.1093/sysbio/sys062 10.1016/j.tcs.2006.06.022 10.1016/j.tcs.2004.12.012 10.1093/oso/9780198509424.001.0001 10.1007/978-3-540-87361-7_25 10.1007/BFb0030789
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Keywords	Phylogenetic network NP-hard Supernetwork Phylogenetic tree Exponential-time algorithm Polynomial-time algorithm Trinet Aho algorithm
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Snippet	Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1... Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1...
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Bioinformatics Computer Science Computer Systems Organization and Communication Networks Data Structures and Information Theory Mathematics of Computing Networks Phylogenetics Polynomials Theory of Computation
Title	Reconstructing Phylogenetic Level-1 Networks from Nondense Binet and Trinet Sets
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