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Estimating the history of a random recursive tree
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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.
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Cited by 3 Pith papers
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Finding the root in random nearest neighbor trees
For random nearest neighbor trees, the root can be found among a confidence set of size roughly log(1/epsilon) divided by log log(1/epsilon) in one dimension.
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A Proof of The Changepoint Detection Threshold Conjecture in Preferential Attachment Models
Changepoint detection in preferential attachment networks is impossible when the change occurs in the last o(√n) steps, resolving the Bet-Castro-van der Hofstad conjecture.
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Subcritical percolation and network archaeology on random recursive tree substrate networks
For random recursive trees with independent Erdős–Rényi shortcut edges, subcritical bond percolation exposes a decorated tree structure on which Jordan centrality recovers the root within a deterministic-size confidence set.
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