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：本文研究了在随机递归树中估计顶点到达顺序的问题。具体而言，我们研究了两种基本模型：均匀连接模型和线性优先连接模型。我们提出了一种基于Jordan中心性度量的顺序估计器，并定义了一族风险度量来量化排序过程的质量。此外，我们建立了该问题的极小化极大下界，并证明了所提出的估计器近乎最优。最后，我们通过数值实验表明，所提出的估计器优于基于度数和谱的排序方法。