On the complexity of distance-based evolutionary tree reconstruction
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Analytic solutions for three taxon ML trees with variable rates across sites
Discrete Applied Mathematics
Phylogenies without Branch Bounds: Contracting the Short, Pruning the Deep
RECOMB 2'09 Proceedings of the 13th Annual International Conference on Research in Computational Molecular Biology
Alignment-Free phylogenetic reconstruction
RECOMB'10 Proceedings of the 14th Annual international conference on Research in Computational Molecular Biology
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We give a greedy learning algorithm for reconstructing an evolutionary tree based on a certain harmonic average on triplets of terminal taxa. After the pairwise distances between terminal taxa are estimated from sequence data, the algorithm runs in $\smallbigO{\numtaxa^2}$ time using $\smallbigO{\numtaxa}$ work space, where $\numtaxa$ is the number of terminal taxa. These time and space complexities are optimal in the sense that the size of an input distance matrix is $\numtaxa^2$ and the size of an output tree is $\numtaxa$. Moreover, in the Jukes--Cantor model of evolution, the algorithm recovers the correct tree topology with high probability using sample sequences of length polynomial in (1) $\numtaxa$, (2) the logarithm of the error probability, and (3) the inverses of two small parameters.