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Leaf Stripping on Uniform Attachment Trees

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arxiv 2410.06481 v1 pith:AZ624IFR submitted 2024-10-09 math.PR cs.DScs.LGstat.ML

Louigi Addario-Berry , Anna Brandenberger , Simon Briend , Nicolas Broutin , Gábor Lugosi This is my paper · ORCID
classification math.PRcs.DScs.LGstat.ML
keywords algorithmattachmentepsilonsizetreetreesuniformanalyze
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abstract

In this note we analyze the performance of a simple root-finding algorithm in uniform attachment trees. The leaf-stripping algorithm recursively removes all leaves of the tree for a carefully chosen number of rounds. We show that, with probability $1 - \epsilon$, the set of remaining vertices contains the root and has a size only depending on $\epsilon$ but not on the size of the tree.

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Cited by 1 Pith paper

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  1. Subcritical percolation and network archaeology on random recursive tree substrate networks

    math.PR 2026-07 accept novelty 5.0 of 10

    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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