Abstract
Given a distance matrix M that represents evolutionary distances between any two species, an edge-weighted phylogenetic network N is said to satisfy M if between any pair of species, there exists a path in N with length equal to the corresponding entry in M. In this paper, we consider a special class of networks called 1-articulated network which is a proper superset of galled trees. We show that if the distance matrix M is derived from an ultrametric 1-articulated network N (i.e., for any species X and Y, the entry M(X, Y) is equal to the shortest distance between X and Y in N), we can re-construct an network that satisfies M in \(O(n^2)\) time, where n denotes the number of species; furthermore, the reconstructed network is guaranteed to be the simplest, in a sense that the number of hybrid nodes is minimized. In addition, one may easily index a 1-articulated network N with minimum number of hybrid nodes in O(n) space, such that on given any phylogenetic tree T, we can determine if T is contained in N (i.e., if a spanning subtree \(T'\) of N is a subdivision of T) in O(n) time.
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Bender, M.A., Farach-Colton, M., Pemmasani, G., Skiena, S., Sumazin, P.: Lowest common ancestors in trees and directed acyclic graphs. J. Algorithms 57(2), 75–94 (2005)
Bordewich, M., Tokac, N.: An algorithm for reconstructing ultrametric tree-child networks from inter-taxa distances. DAM 213, 47–59 (2016)
Bryant, D., Moulton, V.: Neighbor-net: an agglomerative method for the construction of phylogenetic networks. Mol. Biol. Evol. 21(2), 255–265 (2004)
Cardona, G., Rossello, F., Valiente, G.: Comparison of tree-child phylogenetic networks. IEEE/ACM TCBB 6(4), 552–569 (2009)
Chan, H., Jansson, J., Lam, T., Yiu, S.: Reconstructing an ultrametric galled phylogenetic network from a distance matrix. JBCB 4(4), 807–832 (2006)
Day, W.H.E.: Optimal algorithms for comparing trees with labeled leaves. J. Classif. 2(1), 7–28 (1985)
Gambette, P., Gunawan, A.D.M., Labarre, A., Vialette, S., Zhang, L.: Locating a tree in a phylogenetic network in quadratic time. In: Przytycka, T.M. (ed.) RECOMB 2015. LNCS, vol. 9029, pp. 96–107. Springer, Cham (2015). doi:10.1007/978-3-319-16706-0_12
Gusfield, D., Eddhu, S., Langley, C.H.: Optimal, efficient reconstruction of phylogenetic networks with constrained recombination. JBCB 2(1), 173–214 (2004)
Huson, D.H., Klöpper, T.H.: Beyond galled trees - decomposition and computation of galled networks. In: Speed, T., Huang, H. (eds.) RECOMB 2007. LNCS, vol. 4453, pp. 211–225. Springer, Heidelberg (2007). doi:10.1007/978-3-540-71681-5_15
Huynh, T.N.D., Jansson, J., Nguyen, N.B., Sung, W.-K.: Constructing a smallest refining galled phylogenetic network. In: Miyano, S., Mesirov, J., Kasif, S., Istrail, S., Pevzner, P.A., Waterman, M. (eds.) RECOMB 2005. LNCS, vol. 3500, pp. 265–280. Springer, Heidelberg (2005). doi:10.1007/11415770_20
van Iersel, L., Semple, C., Steel, M.: Locating a tree in a phylogenetic network. IPL 110(23), 1037–1043 (2010)
Jansson, J., Sung, W.: Inferring a level-1 phylogenetic network from a dense set of rooted triplets. TCS 363(1), 60–68 (2006)
van Iersel, L., Keijsper, J., Kelk, S., Stougie, L., Hagen, F., Boekhout, T.: Constructing level-2 phylogenetic networks from triplets. IEEE/ACM TCBB 6(4), 667–681 (2009)
Nakhleh, L., Warnow, T., Linder, C.R.: Reconstructing reticulate evolution in species: theory and practice. JCB 12(6), 796–811 (2005)
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Chang, KY., Cui, Y., Yiu, SM., Hon, WK. (2017). Reconstructing One-Articulated Networks with Distance Matrices. In: Cai, Z., Daescu, O., Li, M. (eds) Bioinformatics Research and Applications. ISBRA 2017. Lecture Notes in Computer Science(), vol 10330. Springer, Cham. https://doi.org/10.1007/978-3-319-59575-7_4
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DOI: https://doi.org/10.1007/978-3-319-59575-7_4
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