On the optimality of the neighbor-joining algorithm.

The popular neighbor-joining (NJ) algorithm used in phylogenetics is a greedy algorithm for finding the balanced minimum evolution (BME) tree associated to a dissimilarity map. From this point of view, NJ is "optimal" when the algorithm outputs the tree which minimizes the balanced minimum evolution criterion. We use the fact that the NJ tree topology and the BME tree topology are determined by polyhedral subdivisions of the spaces of dissimilarity maps [equation; see text] to study the optimality of the neighbor-joining algorithm. In particular, we investigate and compare the polyhedral subdivisions for n