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Lichen Bao and
Sergey Bereg. Counting Faces in Split Networks. In ISBRA09, Vol. 5251:284-295 of LNCS, 2009. Note: http://dx.doi.org/10.1007/978-3-642-01551-9_12.
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SplitsTree is a popular program for inferring and visualizing various phylogenetic networks including split networks. Split networks are useful for realizing metrics that are linear combinations of split metrics. We show that the realization is not unique in some cases and design an algorithm for computing split networks with minimum number of faces. We also prove that the minimum number of faces in a split network is equal to the number of pairs of incompatible splits.
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Lichen Bao and
Sergey Bereg. Clustered SplitsNetworks. In COCOA08, Vol. 5165:469-478 of LNCS, springer, 2008. Keywords: abstract network, from distances, NeighborNet, realization, reconstruction. Note: http://dx.doi.org/10.1007/978-3-540-85097-7_44, slides available at http://www.utdallas.edu/~besp/cocoa08talk.pdf.
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"We address the problem of constructing phylogenetic networks using two criteria: the number of cycles and the fit value of the network. Traditionally the fit value is the main objective for evaluating phylogenetic networks. However, a small number of cycles in a network is desired and pointed out in several publications. We propose a new phylogenetic network called CS-network and a method for constructing it. The method is based on the well-known splitstree method. A CS-network contains a face which is k-cycle, k ≥ 3 (not as splitstree). We discuss difficulties of using non-parallelogram faces in splitstree networks. Our method involves clustering and optimization of weights of the network edges. The algorithm for constructing the underlying graph (except the optimization step) has a polynomial time. Experimental results show a good performance of our algorithm. © Springer-Verlag Berlin Heidelberg 2008."
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