A Cluster Reduction for Computing the Subtree Distance Between Phylogenies

Calculating the rooted subtree prune and regraft (rSPR) distance between two rooted binary phylogenetic trees is a frequently applied process in various areas of molecular evolution. However, computing this distance is an NP-hard problem and practical algorithms for computing it exactly are rare. In this paper, a divide-and-conquer approach to calculating the rSPR distance is established. This approach breaks the problem instance into a number of smaller and more tractable subproblems. Two reduction rules which were previously used to show that computing the rSPR distance is fixed-parameter tractable can easily be used to complement this new theoretical result, and so a significant positive impact on the running time of calculating this distance in practice is likely.