A simpler linear-time algorithm for the common refinement of rooted phylogenetic trees on a common leaf set

BACKGROUND: The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set L is known to be solvable in linear time. Existing approaches refine one input tree using information of the others and then test whether the results are isomorphic. RESULTS: An O(k|L|) algorithm, LinCR, for constructing the common refinement T of k input trees with a common leaf set L is proposed that explicitly computes the parent function of T in a bottom-up approach. CONCLUSION: LinCR is simpler to implement than other asymptotically optimal algorithms for the problem and outperforms the alternatives in empirical comparisons. AVAILABILITY: An implementation of LinCR in Python is freely available at https://github.com/david-schaller/tralda.