Electronic Journal of Probability

Finding the seed of uniform attachment trees

Gábor Lugosi and Alan S. Pereira

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 18, 15 pp.

Dates
Received: 5 January 2018
Accepted: 22 January 2019
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1551323285

Digital Object Identifier
doi:10.1214/19-EJP268

Mathematical Reviews number (MathSciNet)
MR3925458

Zentralblatt MATH identifier
07055656

Subjects
Primary: NA

Keywords
random trees uniform attachment discrete probability seed

Rights
Creative Commons Attribution 4.0 International License.

Citation

Lugosi, Gábor; Pereira, Alan S. Finding the seed of uniform attachment trees. Electron. J. Probab. 24 (2019), paper no. 18, 15 pp. doi:10.1214/19-EJP268. https://projecteuclid.org/euclid.ejp/1551323285


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