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Recovering evolutionary trees through harmonic greedy triplets

We give a greedy learning algorithm for reconstructing an evolutionary tree based on a harmonic average on triplets of taxa. This algorithm runs in polynomial time in the input size. Using the Jukes-Cantor model of evolution, our algorithm is mathematically proven to require sample sequences of only polynomial lengths in the number of taxa in order to recover the correct tree topology with high probability. In addition to recovering the topology, the algorithm also estimates the tree edge lengths with high accuracy. Our theoretical analysis is supported by simulated experiments, in which the algorithm has demonstrated high success rates, in reconstructing a large tree from short sequences.