Fast Local Search for Unrooted Robinson-Foulds Supertrees

A Robinson-Foulds (RF) supertree for a collection of input trees is a comprehensive species phylogeny that is at minimum total RF distance to the input trees. Thus, an RF supertree is consistent with the maximum number of splits in the input trees. Constructing rooted and unrooted RF supertrees is NP-hard. Nevertheless, effective local search heuristics have been developed for the restricted case where the input trees and the supertree are rooted. We describe new heuristics, based on the Edge Contract and Reline (ECR) operation, that remove this restriction, thereby expanding the utility of RF supertrees. We demonstrate that our local search algorithms yield supertrees with notably better scores than those obtained from rooted heuristics.