Abstract
The number of non-shared edges of two phylogenies is a basic measure of the dissimilarity between the phylogenies. The non-shared edge distance is also a building block for approximating a more sophisticated measure called the nearest neighbor interchange (NNI) distance. In this paper, we give the first sub-quadratic time algorithm for computing the non-shared edge distance, whose running time is O(nlogn). Based on this result, we can speed up the existing approximation algorithm for the NNI distance from O(n 2 ) time to O(nlogn) time. © 2004 Elsevier B.V. All rights reserved.