Abstract
The rooted triplet distance is a measure of the dissimilarity of two phylogenetic trees with identical leaf label sets. An algorithm by Brodal et al. [2] that computes it in \(O(n \log n)\) time, where n is the number of leaf labels, has recently been implemented in the software package tqDist [14]. In this paper, we show that replacing the hierarchical decomposition tree used in Brodal et al.’s algorithm by a centroid paths-based data structure yields an \(O(n \log ^{3} n)\)-time algorithm that, although slower in theory, is easier to implement and apparently faster in practice. Simulations for values of n up to 1, 000, 000 support our claims experimentally.
J. Jansson—Funded by The Hakubi Project and KAKENHI grant number 26330014.
R. Rajaby—Funded by the EXTRA Project at the University of Milano-Bicocca.
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References
Bansal, M.S., Dong, J., Fernández-Baca, D.: Comparing and aggregating partially resolved trees. Theor. Comput. Sci. 412(48), 6634–6652 (2011)
Brodal, G.S., Fagerberg, R., Mailund, T., Pedersen, C.N.S., Sand, A.: Efficient algorithms for computing the triplet and quartet distance between trees of arbitrary degree. In: Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2013), pp. 1814–1832. SIAM (2013)
Cole, R., Farach-Colton, M., Hariharan, R., Przytycka, T., Thorup, M.: An \({O}(n \log n)\) algorithm for the maximum agreement subtree problem for binary trees. SIAM J. Comput. 30(5), 1385–1404 (2000)
Critchlow, D.E., Pearl, D.K., Qian, C.: The triples distance for rooted bifurcating phylogenetic trees. Syst. Biol. 45(3), 323–334 (1996)
Dobson, A.J.: Comparing the shapes of trees. In: Street, A.P., Wallis, W.D. (eds.) Combinatorial Mathematics III. LNM, vol. 452, pp. 95–100. Springer-Verlag, Heidelberg (1975)
Estabrook, G.F., McMorris, F.R., Meacham, C.A.: Comparison of undirected phylogenetic trees based on subtrees of four evolutionary units. Syst. Zool. 34(2), 193–200 (1985)
Felsenstein, J.: Inferring Phylogenies. Sinauer Associates Inc, Sunderland (2004)
Fenwick, P.M.: A new data structure for cumulative frequency tables. Softw.: Pract. Experience 24(3), 327–336 (1994)
Gusfield, D., Eddhu, S., Langley, C.: Optimal, efficient reconstruction of phylogenetic networks with constrained recombination. J. Bioinform. Comput. Biol. 2(1), 173–213 (2004)
Holt, M.K., Johansen, J., Brodal, G.S.: On the scalability of computing triplet and quartet distances. In: Proceedings of the 16th Workshop on Algorithm Engineering and Experiments (ALENEX 2014), pp. 9–19. SIAM (2014)
Jansson, J., Lingas, A.: Computing the rooted triplet distance between galled trees by counting triangles. J. Discrete Algorithms 25, 66–78 (2014)
McKenzie, A., Steel, M.: Distributions of cherries for two models of trees. Math. Biosci. 164(1), 81–92 (2000)
Nethercote, N., Seward, J.: Valgrind: a framework for heavyweight dynamic binary instrumentation. In: Proceedings of the ACM SIGPLAN 2007 Conference on Programming Language Design and Implementation (PLDI 2007), pp. 89–100. ACM (2007)
Sand, A., Holt, M.K., Johansen, J., Brodal, G.S., Mailund, T., Pedersen, C.N.S.: tqDist: a library for computing the quartet and triplet distances between binary or general trees. Bioinformatics 30(14), 2079–2080 (2014)
sparsehash project webpage. https://code.google.com/p/sparsehash/
Documentation for unordered_map. http://www.cplusplus.com/reference/unordered_map/unordered_map/
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Jansson, J., Rajaby, R. (2015). A More Practical Algorithm for the Rooted Triplet Distance. In: Dediu, AH., Hernández-Quiroz, F., Martín-Vide, C., Rosenblueth, D. (eds) Algorithms for Computational Biology. AlCoB 2015. Lecture Notes in Computer Science(), vol 9199. Springer, Cham. https://doi.org/10.1007/978-3-319-21233-3_9
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