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 distance (dissimilarity) between the phylogenies. The non-shared edges are also the building block for approximating a more sophisticated metric called the NNI distance. In this paper we give the first sub-quadratic time algorithm for finding the non-shared edges, which are then used to speed up the existing approximation algorithm for the NNI distance. The time is improved from O(n2) to O(n log n). Another popular distance metric for phylogenies is the STT distance. Previous work on computing the STT distance focused on degree-3 trees only. We show that the STT distance can be applied in a broader sense, allowing us to cover degree-d trees, where d ≥ 3. In particular, we give a new approximation algorithm for the STT distance.