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.
"Finding the seed of uniform attachment trees." Electron. J. Probab. 24 1 - 15, 2019. https://doi.org/10.1214/19-EJP268