Fast FPT Algorithms for Computing Rooted Agreement Forests: Theory and Experiments

We improve on earlier FPT algorithms for computing a rooted maximum agreement forest (MAF) or a maximum acyclic agreement forest (MAAF) of a pair of phylogenetic trees. Their sizes give the subtree-prune-and-regraft (SPR) distance and the hybridization number of the trees, respectively. We introduce new branching rules that reduce the running time of the algorithms from O(3n) and O(3n logn) to O(2.42n) and O(2.42n logn), respectively. In practice, the speed up of the algorithms may be much more than predicted by the worst-case analysis. We confirm this intuition experimentally by computing MAFs for simulated trees and trees inferred from protein sequence data. We show that our MAF algorithm is orders of magnitude faster than the best previous methods and can handle much larger trees and SPR distances.