Abstract
The fastest known algorithms for computing the R* consensus tree of \(k\) rooted phylogenetic trees with \(n\) leaves each and identical leaf label sets run in \(O(n^{2} \sqrt{\log n})\) time when \(k = 2\) (ref. [10]) and \(O(k n^{3})\) time when \(k \ge 3\) (ref. [4]). This paper shows how to compute it in \(O(n^{2})\) time for \(k = 2\), \(O(n^{2} \log ^{4/3} n)\) time for \(k = 3\), and \(O(n^{2} \log ^{k+2} n)\) time for unbounded \(k\).
Jesper Jansson: Funded by The Hakubi Project and KAKENHI grant number 26330014.
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References
Bansal, M.S., Dong, J., Fernández-Baca, D.: Comparing and aggregating partially resolved trees. Theoretical Computer Science 412(48), 6634–6652 (2011)
Bender, M.A., Farach-Colton, M.: The LCA problem revisited. In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, pp. 88–94. Springer, Heidelberg (2000)
Bender, M.A., Farach-Colton, M.: The Level Ancestor Problem simplified. Theoretical Computer Science 321(1), 5–12 (2004)
Bryant, D.: A classification of consensus methods for phylogenetics. In: Janowitz, M.F., Lapointe, F.-J., McMorris, F.R., Mirkin, B., Roberts, F.S. (eds.) Bioconsensus. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 61, pp. 163–184. American Mathematical Society (2003)
Bryant, D., Berry, V.: A structured family of clustering and tree construction methods. Advances in Applied Mathematics 27(4), 705–732 (2001)
Chan, T.M., Pǎtraşcu, M.: Counting inversions, offline orthogonal range counting, and related problems. In: Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2010), pp. 161–173. SIAM (2010)
Degnan, J.H., DeGiorgio, M., Bryant, D., Rosenberg, N.A.: Properties of consensus methods for inferring species trees from gene trees. Systematic Biology 58(1), 35–54 (2009)
Felsenstein, J.: Inferring Phylogenies. Sinauer Associates Inc., Sunderland (2004)
Harel, D., Tarjan, R.E.: Fast algorithms for finding nearest common ancestors. SIAM Journal on Computing 13(2), 338–355 (1984)
Jansson, J., Sung, W.-K.: Constructing the R* consensus tree of two trees in subcubic time. Algorithmica 66(2), 329–345 (2013)
Kannan, S., Warnow, T., Yooseph, S.: Computing the local consensus of trees. SIAM Journal on Computing 27(6), 1695–1724 (1998)
Lee, C.-M., Hung, L.-J., Chang, M.-S., Shen, C.-B., Tang, C.-Y.: An improved algorithm for the maximum agreement subtree problem. Information Processing Letters 94(5), 211–216 (2005)
Sung, W.-K.: Algorithms in Bioinformatics: A Practical Introduction. Chapman & Hall/CRC (2010)
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Jansson, J., Sung, WK., Vu, H., Yiu, SM. (2014). Faster Algorithms for Computing the R* Consensus Tree. In: Ahn, HK., Shin, CS. (eds) Algorithms and Computation. ISAAC 2014. Lecture Notes in Computer Science(), vol 8889. Springer, Cham. https://doi.org/10.1007/978-3-319-13075-0_33
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DOI: https://doi.org/10.1007/978-3-319-13075-0_33
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