Fast Compatibility Testing for Phylogenies with Nested Taxa

Semi-labeled trees are phylogenies whose internal nodes may be labeled by higher-order taxa. Thus, a leaf labeled Mus musculus could nest within a subtree whose root node is labeled Rodentia, which itself could nest within a subtree whose root is labeled Mammalia. Suppose we are given collection P of semi-labeled trees over various subsets of a set of taxa. The ancestral compatibility problem asks whether there is a semi-labeled tree T that respects the clusterings and the ancestor/descendant relationships implied by the trees in P. We give a (O) over tilde (M-P) algorithm for the ancestral compatibility problem, where MP is the total number of nodes and edges in the trees in P. Unlike the best previous algorithm, the running time of our method does not depend on the degrees of the nodes in the input trees.