Fast error-tolerant quartet phylogeny algorithms

We present a quartet-based phylogeny algorithm that returns the correct topology for n taxa in O(nlogn) time with high probability, assuming that each quartet is inconsistent with the true tree topology with constant probability, independent of other quartets. Our incremental algorithm relies upon a search tree structure for the phylogeny that is balanced, with high probability, no matter the true topology. In experiments, our prototype was as fast as the fastest heuristics, but because real data do not typically satisfy our probabilistic assumptions, its overall performance is not as good as our theoretical results predict.