On the discovery of the seed in uniform attachment trees

TL;DR

This paper explores methods to identify the seed in uniform attachment trees, focusing on confidence sets and leaf identification, to improve understanding of seed structure with probabilistic guarantees.

Contribution

It introduces new techniques for seed detection and leaf identification in uniform attachment trees based on seed properties and internal node positions.

Findings

Developed confidence sets for seed inclusion with probabilistic guarantees

Proposed algorithms for seed leaf identification given internal node positions

Enhanced understanding of seed structure in uniform attachment trees

Abstract

We investigate the size of vertex confidence sets for including part of (or the entirety of) the seed in seeded uniform attachment trees, given knowledge of some of the seed's properties, and with a prescribed probability of failure. We also study the problem of identifying the leaves of a seed in a seeded uniform attachment tree, given knowledge of the positions of all internal nodes of the seed.