DAG-type Distributed Ledgers via Young-age Preferential Attachment

TL;DR

This paper models DAG-type distributed ledgers using a Young-age Preferential Attachment scheme, analyzing their degree structure and conditions for large connected components, to improve understanding of system scalability.

Contribution

It introduces a recursive model for DAG-based ledgers based on young-age preference, providing insights into their asymptotic degree distribution and connectivity properties.

Findings

A mathematical model for DAG-based ledgers using Young-age Preferential Attachment.

The asymptotic degree structure of the resulting graph is characterized.

A large forward component emerges under certain edge density conditions.

Abstract

Distributed Ledger Technologies provide a mechanism to achieve ordering among transactions that are scattered on multiple participants with no prerequisite trust relations. This mechanism is essentially based on the idea of new transactions referencing older ones in a chain structure. Recently, DAG-type Distributed Ledgers that are based on directed acyclic graphs (DAGs) were proposed to increase the system scalability through sacrificing the total order of transactions. In this paper, we develop a mathematical model to study the process that governs the addition of new transactions to the DAG-type Distributed Ledger. We propose a simple model for DAG-type Distributed Ledgers that are obtained from a recursive Young-age Preferential Attachment scheme, i.e. new connections are made preferably to transactions that have not been in the system for very long. We determine the asymptotic degree structure of the resulting graph and show that a forward component of linear size arises if the edge density is chosen sufficiently large in relation to the `young-age preference' that tunes how quickly old transactions become unattractive.