Computing Triplet and Quartet Distances Between Trees

Gerth Stølting Brodal

Aarhus University, MADALGO

Abstract

The triplet and quartet distances are distance measures to compare two rooted and two unrooted trees, respectively. The leaves of the two trees should have the same set of n labels. The distances are defined by enumerating all subsets of three labels (triplets) and four labels (quartets), respectively, and counting how often the induced topologies in the two input trees are different. We will present efficient algorithms for computing these distances, and how to compute the triplet distance in time O(n log n) and the quartet distance in time O(dn log n), where d is the maximal degree of any node in the two trees. Within the same time bounds, our framework also allows us to compute the parameterized triplet and quartet distances, where a parameter is introduced to weight resolved (binary) topologies against unresolved (non-binary) topologies. The previous best algorithm for