Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A few logs suffice to build (almost) all trees: part II
Theoretical Computer Science
On the complexity of distance-based evolutionary tree reconstruction
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Fast and reliable reconstruction of phylogenetic trees with very short edges
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
Towards a practical O(n log n) phylogeny algorithm
WABI'11 Proceedings of the 11th international conference on Algorithms in bioinformatics
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
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We present the first sub-quadratic time algorithm that with high probability correctly reconstructs phylogenetic trees for short sequences generated by a Markov model of evolution. Due to rapid expansion in sequence databases, such very fast algorithms are necessary. Other fast heuristics have been developed for building trees from large alignments [18,1], but they lack theoretical performance guarantees. Our new algorithm runs in O(n1+γ(g)log2n) time, where γ is an increasing function of an upper bound on the branch lengths in the phylogeny, the upper bound g must be below $1/2-\sqrt{1/8} \approx 0.15$, and γ(g)g. For phylogenies with very short branches, the running time of our algorithm is near-linear. For example, if all branches have mutation probability less than 0.02, the running time of our algorithm is roughly O(n1.2log2n). Our preliminary experiments show that many large phylogenies can be reconstructed more accurately than allowed by current methods, in comparable running times.