Isomorphism Testing of Rooted Trees in Linear Time

Abstract: The AHU-algorithm solves the computationally difficult graph isomorphism problem for rooted trees, and does so with a linear time complexity. Although the AHU-algorithm has remained state of the art for almost 50 years, it has been criticized for being unclearly presented, and no complete proof of correctness has been given. In this text, that gap is filled: we formalize the algorithm's main point of assigning and compressing labels to provide a characterization of isomorphic rooted trees, and then proceed with proving the correctness and optimal runtime of the AHU-algorithm.