Growth of Random Trees by Leaf Attachment
Data Structures and Algorithms
2020-11-03 v3 Cryptography and Security
Probability
Applications
Abstract
We study the growth of a time-ordered rooted tree by probabilistic attachment of new vertices to leaves. We construct a likelihood function of the leaves based on the connectivity of the tree. We take such connectivity to be induced by the merging of directed ordered paths from leaves to the root. Combining the likelihood with an assigned prior distribution leads to a posterior leaf distribution from which we sample attachment points for new vertices. We present computational examples of such Bayesian tree growth. Although the discussion is generic, the initial motivation for the paper is the concept of a distributed ledger, which may be regarded as a time-ordered random tree that grows by probabilistic leaf attachment.
Keywords
Cite
@article{arxiv.2010.05589,
title = {Growth of Random Trees by Leaf Attachment},
author = {Nomvelo Sibisi},
journal= {arXiv preprint arXiv:2010.05589},
year = {2020}
}