# Shallow Overlay Trees Suffice for High-Throughput Consensus

## TL;DR

This paper demonstrates that shallow overlay multicast trees with heights up to two are sufficient to achieve optimal throughput in all-to-all data transmission within WANs, improving blockchain system performance.

## Contribution

It proves that shallow broadcast trees are sufficient for optimal throughput in congestion-free core network models for all-to-all data transmission.

## Key findings

- Shallow trees (height ≤ 2) suffice for optimal throughput.
- Optimal throughput is achievable with shallow overlay multicast.
- The approach benefits blockchain data transmission performance.

## Abstract

All-to-all data transmission is a typical data transmission pattern in blockchain systems. Developing an optimization scheme that provides high throughput and low latency data transmission can significantly benefit the performance of those systems. In this work, we consider the problem of optimizing all-to-all data transmission in a wide area network(WAN) using overlay multicast. We prove that in a congestion-free core network model, using shallow broadcast trees with heights up to two is sufficient for all-to-all data transmission to achieve the optimal throughput allowed by the available network resources.