Estimating the history of a random recursive tree

• Authors: Simon Briend, Christophe Giraud, Gábor Lugosi and Déborah Sulem
• Bernoulli, Vol. 31, No. 4, 3260–3284, 3260–3284

This paper studies the problem of estimating the order of arrival of the vertices in a random recursive tree. Specifically, we study two fundamental models: the uniform attachment model and the linear preferential attachment model. We propose an order estimator based on the Jordan centrality measure and define a family of risk measures to quantify the quality of the ordering procedure. Moreover, we establish a minimax lower bound for this problem, and prove that the proposed estimator is nearly optimal. Finally, we numerically demonstrate that the proposed estimator outperforms degree-based and spectral ordering procedure.