An algebraic metric for phylogenetic trees

The definition of similarity measures for phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in databases, and the assessment of phylogenetic reconstruction methods. The transposition distance for fully resolved trees is a recent addition to the extensive collection of available metrics for comparing phylogenetic trees. In this work, we generalize the transposition metric from fully resolved to arbitrary phylogenetic trees, through a construction that involves an embedding of the set of phylogenetic trees (up to isomorphisms) with a fixed number of labeled leaves into a symmetric group. We also show that this transposition distance can be computed in linear time and we establish some of its basic properties.