The Computational Complexity of the Unrooted Subtree Prune and Regraft Distance

We show that computation of the subtree prune and regraft (SPR) distance between unrooted binary phylogenetic trees is NP-Hard and fixed parameter tractable. Similar results exist for the related tree bisection and reconnection (TBR) distance, as well as the SPR distance between rooted trees but the complexity of the unrooted SPR case has heretofore remained unknown.