Improved Phylogeny Comparisons: Non-shared Edges, Nearest Neighbor Interchanges, and Subtree Transfers

The number of the non-shared edges of two phylogenies is a basic measure of the dissimilarity between the phylogenies. The non-shared edges are also the building block for approximating a more sophisticated metric called the nearest neighbor interchange (NNI) distance. In this paper, we give the rst subquadratic-time algorithm for nding the non-shared edges, which are then used to speed up the existing approximating algorithm for the NNI distance from O(n2) time to O(n log n) time. Another popular distance metric for phylogenies is the subtree transfer (STT) distance. Previous work on computing the STT distance considered degree-3 trees only. We give an approximation algorithm for the STT distance for degree-d trees with arbitrary d and with generalized STT operations.