Finding the seed of uniform attachment trees

TL;DR

This paper explores methods to recover the initial seed tree in uniform attachment trees, analyzing algorithms for different seed types to understand how well the original structure can be identified from large observed trees.

Contribution

It introduces and analyzes seed-finding algorithms for different seed structures in uniform attachment trees, advancing understanding of seed recovery.

Findings

Algorithms can partially recover seed trees from large uniform attachment trees.

Recovery effectiveness varies with seed type (path, star, random).

Theoretical bounds on seed identification success are established.

Abstract

A uniform attachment tree is a random tree that is generated dynamically. Starting from a fixed "seed" tree, vertices are added sequentially by attaching each vertex to an existing vertex chosen uniformly at random. Upon observing a large (unlabeled) tree, one wishes to find the initial seed. We investigate to what extent seed trees can be recovered, at least partially. We consider three types of seeds: a path, a star, and a random uniform attachment tree. We propose and analyze seed-finding algorithms for all three types of seed trees.