Fast Compatibility Testing for Phylogenies with Nested Taxa

TL;DR

This paper introduces a fast algorithm for testing compatibility among semi-labeled phylogenetic trees with nested taxa, improving efficiency by removing dependence on node degrees.

Contribution

The authors present a new $ ilde{O}(M_{ ext{P}})$ algorithm for ancestral compatibility that is faster and less dependent on node degrees than previous methods.

Findings

Algorithm runs in near-linear time relative to total nodes and edges.

Performance is independent of node degrees in input trees.

Provides a practical tool for phylogenetic compatibility testing.

Abstract

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 $\mathcal P$ of semi-labeled trees over various subsets of a set of taxa. The ancestral compatibility problem asks whether there is a semi-labeled tree $\mathcal T$ that respects the clusterings and the ancestor/descendant relationships implied by the trees in $\mathcal P$. We give a $\tilde{O}(M_{\mathcal{P}})$ algorithm for the ancestral compatibility problem, where $M_{\mathcal{P}}$ is the total number of nodes and edges in the trees in $\mathcal P$. Unlike the best previous algorithm, the running time of our method does not depend on the degrees of the nodes in the input trees.