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Regular Networks Can be Uniquely Constructed from Their Trees
May/June 2011 (vol. 8 no. 3)
pp. 785-796
Stephen J. Willson, Iowa State University, Ames
A rooted acyclic digraph N with labeled leaves displays a tree T when there exists a way to select a unique parent of each hybrid vertex resulting in the tree T. Let Tr(N) denote the set of all trees displayed by the network N. In general, there may be many other networks M, such that Tr(M) = Tr(N). A network is regular if it is isomorphic with its cover digraph. If N is regular and {\cal D} is a collection of trees displayed by N, this paper studies some procedures to try to reconstruct N given {\cal D}. If the input is {\cal D}=Tr(N), one procedure is described, which will reconstruct N. Hence, if N and M are regular networks and Tr(N) = Tr(M), it follows that N = M, proving that a regular network is uniquely determined by its displayed trees. If {\cal D} is a (usually very much smaller) collection of displayed trees that satisfies certain hypotheses, modifications of the procedure will still reconstruct N given {\cal D}.

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Index Terms:
Phylogeny, phylogenetic, network, tree, regular, hybrid.
Stephen J. Willson, "Regular Networks Can be Uniquely Constructed from Their Trees," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 3, pp. 785-796, May-June 2011, doi:10.1109/TCBB.2010.69
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