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 procedures.

翻译：本文研究随机递归树中顶点到达顺序的估计问题。具体而言，我们研究两个基本模型：均匀附着模型与线性优先附着模型。我们提出一种基于Jordan中心性测度的顺序估计器，并定义了一族风险测度以量化排序过程的质量。此外，我们建立了该问题的极小极大下界，并证明所提估计器具有近似最优性。最后，我们通过数值实验证明所提估计器在性能上优于基于度数与谱方法的排序算法。