Abstract
Reconstructing phylogenetic trees efficiently and accurately from distance estimates is an ongoing challenge in computational biology from both practical and theoretical considerations. We study algorithms which are based on a characterization of edge-weighted trees by distances to LCAs ({\em Least Common Ancestors}). This characterization enables a direct application of ultrametric reconstruction techniques to trees which are not necessarily ultrametric. A simple and natural neighbor joining criterion based on this observation is used to provide a family of efficient neighbor-joining algorithms. These algorithms are shown to reconstruct a refinement of the Buneman tree, which implies optimal robustness to noise under criteria defined by Atteson. In this sense, they outperform many popular algorithms such as Saitou\&Nei's NJ. Preliminary experimental results indicate that when executed from an appropriate root taxon, this algorithm provides reconstruction of phylogenies which are competitive with NJ and other common algorithms.