A More Practical Algorithm for the Rooted Triplet Distance

Abstract

The rooted triplet distance is a measure of the dissimilarity of two phylogenetic trees with identical leaf label sets. An algorithm by Brodal et al.i¾?[2] that computes it in $$On \log n$$Onlogn time, where n is the number of leaf labels, has recently been implemented in the software package tqDisti¾?[14]. In this paper, we show that replacing the hierarchical decomposition tree used in Brodal et al.'s algorithm by a centroid paths-based data structure yields an $$On \log ^{3} n$$Onlog3n-time algorithm that, although slower in theory, is easier to implement and apparently faster in practice. Simulations for values ofi¾?n upi¾?toi¾?1,i¾?000,i¾?000 support our claims experimentally.