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Leo van Iersel,
Charles Semple and
Mike Steel. Locating a tree in a phylogenetic network. In IPL, Vol. 110(23), 2010. Keywords: cluster containment, explicit network, from network, level k phylogenetic network, normal network, NP complete, phylogenetic network, polynomial, regular network, time consistent network, tree containment, tree sibling network, tree-child network. Note: http://arxiv.org/abs/1006.3122.
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"Phylogenetic trees and networks are leaf-labelled graphs that are used to describe evolutionary histories of species. The Tree Containment problem asks whether a given phylogenetic tree is embedded in a given phylogenetic network. Given a phylogenetic network and a cluster of species, the Cluster Containment problem asks whether the given cluster is a cluster of some phylogenetic tree embedded in the network. Both problems are known to be NP-complete in general. In this article, we consider the restriction of these problems to several well-studied classes of phylogenetic networks. We show that Tree Containment is polynomial-time solvable for normal networks, for binary tree-child networks, and for level-k networks. On the other hand, we show that, even for tree-sibling, time-consistent, regular networks, both Tree Containment and Cluster Containment remain NP-complete. © 2010 Elsevier B.V. All rights reserved."
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Mareike Fischer,
Leo van Iersel,
Steven Kelk and
Celine Scornavacca. On Computing The Maximum Parsimony Score Of A Phylogenetic Network. In SIDMA, Vol. 29(1):559-585, 2015. Keywords: APX hard, cluster containment, explicit network, FPT, from network, from sequences, integer linear programming, level k phylogenetic network, NP complete, parsimony, phylogenetic network, phylogeny, polynomial, Program MPNet, reconstruction, software. Note: http://arxiv.org/abs/1302.2430.
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Andreas Gunawan,
Bhaskar DasGupta and
Louxin Zhang. A decomposition theorem and two algorithms for reticulation-visible networks. In Information and Computation, Vol. 252:161-175, 2017. Keywords: cluster containment, explicit network, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, reticulation-visible network, tree containment. Note: https://www.cs.uic.edu/~dasgupta/resume/publ/papers/Infor_Comput_IC4848_final.pdf.
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Luay Nakhleh and
Li-San Wang. Phylogenetic Networks, Trees, and Clusters. In IWBRA05, Vol. 3515:919-926 of LNCS, springer, 2005. Keywords: cluster containment, evaluation, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, tree containment, tree-child network. Note: http://www.cs.rice.edu/~nakhleh/Papers/NakhlehWang.pdf.
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Luay Nakhleh and
Li-San Wang. Phylogenetic Networks: Properties and Relationship to Trees and Clusters. In TCSB2, Vol. 3680:82-99 of LNCS, springer, 2005. Keywords: cluster containment, evaluation, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, tree containment, tree-child network. Note: http://www.cs.rice.edu/~nakhleh/Papers/LNCS_TCSB05.pdf.
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Daniel H. Huson,
Regula Rupp,
Vincent Berry,
Philippe Gambette and
Christophe Paul. Computing Galled Networks from Real Data. In ISMBECCB09, Vol. 25(12):i85-i93 of BIO, 2009. Keywords: abstract network, cluster containment, explicit network, FPT, from clusters, from rooted trees, galled network, NP complete, phylogenetic network, phylogeny, polynomial, Program Dendroscope, reconstruction. Note: http://hal-lirmm.ccsd.cnrs.fr/lirmm-00368545/en/.
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"Motivation: Developing methods for computing phylogenetic networks from biological data is an important problem posed by molecular evolution and much work is currently being undertaken in this area. Although promising approaches exist, there are no tools available that biologists could easily and routinely use to compute rooted phylogenetic networks on real datasets containing tens or hundreds of taxa. Biologists are interested in clades, i.e. groups of monophyletic taxa, and these are usually represented by clusters in a rooted phylogenetic tree. The problem of computing an optimal rooted phylogenetic network from a set of clusters, is hard, in general. Indeed, even the problem of just determining whether a given network contains a given cluster is hard. Hence, some researchers have focused on topologically restricted classes of networks, such as galled trees and level-k networks, that are more tractable, but have the practical draw-back that a given set of clusters will usually not possess such a representation. Results: In this article, we argue that galled networks (a generalization of galled trees) provide a good trade-off between level of generality and tractability. Any set of clusters can be represented by some galled network and the question whether a cluster is contained in such a network is easy to solve. Although the computation of an optimal galled network involves successively solving instances of two different NP-complete problems, in practice our algorithm solves this problem exactly on large datasets containing hundreds of taxa and many reticulations in seconds, as illustrated by a dataset containing 279 prokaryotes. © 2009 The Author(s)."
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Andreas Gunawan,
Bhaskar DasGupta and
Louxin Zhang. Locating a Tree in a Reticulation-Visible Network in Cubic Time. In RECOMB16, Vol. 9649:266 of LNBI, Springer, 2016. Keywords: cluster containment, explicit network, from clusters, from network, from rooted trees, phylogenetic network, phylogeny, polynomial, reticulation-visible network, tree containment. Note: http://arxiv.org/abs/1507.02119.
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Bingxin Lu,
Louxin Zhang and
Hon Wai Leong. A program to compute the soft Robinson-Foulds distance between phylogenetic networks. In APBC17, Vol. 18(Suppl. 2):111 of BMC Genomics, 2017. Keywords: cluster containment, distance between networks, explicit network, exponential algorithm, from network, phylogenetic network, phylogeny, Program icelu-PhyloNetwork. Note: http://dx.doi.org/10.1186/s12864-017-3500-5.
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Louxin Zhang. Recent Progresses in the Combinatorial and Algorithmic Study of Rooted Phylogenetic Networks. In WALCOM20, Vol. 12049:22-27 of LNCS, Springer, 2020. Keywords: cluster containment, galled network, galled tree, nearly-stable network, phylogenetic network, phylogeny, polynomial, reticulation-visible network, survey, time consistent network, tree containment, tree-based network, tree-child network.
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