Who is Who in Phylogenetic Networks

Publications related to 'optimal realization' : The optimal realization of a distance matrix is a graph with weighted edges such that distances in the graph correspond to the distance matrix, and the total weight of edges is minimal.   Order by:   Type | Year

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abstract-network cactus-graph from-distances level-k-phylogenetic-network NP-complete optimal-realization phylogenetic-network phylogeny polynomial realization

2020

1 Momoko Hayamizu, Katharina Huber, Vincent Moulton and Yukihiro Murakami. Recognizing and realizing cactus metrics. In IPL, Vol. 157(105916):1-5, 2020. Keywords: cactus graph, from distances, level k phylogenetic network, optimal realization, polynomial. Note: https://doi.org/10.1016/j.ipl.2020.105916.

2007

2 Alice Lesser. Optimal and Hereditarily Optimal Realizations of Metric Spaces. PhD thesis, Uppsala University, Sweden, 2007. Keywords: from distances, optimal realization, phylogenetic network, phylogeny, realization. Note: http://www.diva-portal.org/diva/getDocument?urn_nbn_se_uu_diva-8297-2__fulltext.pdf.

2001

3 Andreas W. M. Dress, Katharina Huber and Vincent Moulton. Hereditarily Optimal Realizations: Why are they Relevant in Phylogenetic Analysis, and how does one Compute them? In Proceedings of the Euroconference on Algebraic Combinatorics and Applications (Alcoma'99), Pages 110-117, springer, 2001. Keywords: abstract network, from distances, optimal realization, phylogenetic network. Note: http://www.math.uni-bielefeld.de/fsp-math/Preprints/139.pdf.

1986

4 Ingo Althöfer. On optimal realizations of finite metric spaces by graphs. In Discrete and Computational Geometry, Vol. 3(1):103-122, 1986. Keywords: NP complete, optimal realization, realization. Note: http://dx.doi.org/10.1007/BF02187901.         Toggle abstract "Graph realizations of finite metric spaces have widespread applications, for example, in biology, economics, and information theory. The main results of this paper are: 1. Finding optimal realizations of integral metrics (which means all distances are integral) is NP-complete. 2. There exist metric spaces with a continuum of optimal realizations. Furthermore, two conditions necessary for a weighted graph to be an optimal realization are given and an extremal problem arising in connection with the realization problem is investigated. © 1988 Springer-Verlag New York Inc."