An Efficient Algorithm for the Rooted Triplet Distance Between Galled Trees.

Abstract

The previous fastest algorithm for computing the rooted triplet distance between two input galled trees (i.e., phylogenetic networks whose cycles are vertex-disjoint) runs in [Formula: see text] time, where n is the cardinality of the leaf label set. In this article, we present an [Formula: see text]-time solution. Our strategy is to transform the input so that the answer can be obtained by applying an existing [Formula: see text]-time algorithm for the simpler case of two phylogenetic trees a constant number of times. The new algorithm has been implemented, and applying it to pairs of randomly generated galled trees with up to [Formula: see text] leaves confirms that it is fast in practice.