Leaf Stripping on Uniform Attachment Trees

TL;DR

This paper analyzes a leaf-stripping algorithm on uniform attachment trees, demonstrating that it reliably identifies the root with high probability and results in a small remaining vertex set, independent of the tree size.

Contribution

The paper introduces and analyzes a simple root-finding algorithm for uniform attachment trees, showing its effectiveness in identifying the root with high probability.

Findings

The leaf-stripping algorithm correctly identifies the root with probability at least 1 - ε.

The remaining set of vertices after leaf stripping is small and independent of the tree size.

The method provides a probabilistic guarantee for root detection in uniform attachment trees.

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.