# Expander Graph and Communication-Efficient Decentralized Optimization

arXiv: https://arxiv.org/abs/1612.00903 · HTML: https://mlsanity.com/paper/1612.00903/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2016.

## Built on by (most cited first, 7 of 7)

- [Decentralized Federated Learning: Fundamentals, State of the Art, Frameworks, Trends, and Challenges](https://mlsanity.com/paper/2211.08413/) (2022)
- [Exponential Graph is Provably Efficient for Decentralized Deep Training](https://mlsanity.com/paper/2110.13363/) (2021)
- [Refined Convergence and Topology Learning for Decentralized SGD with Heterogeneous Data](https://mlsanity.com/paper/2204.04452/) (2022)
- [Efficient and Reliable Overlay Networks for Decentralized Federated Learning](https://mlsanity.com/paper/2112.15486/) (2021)
- [Adjacent Leader Decentralized Stochastic Gradient Descent](https://mlsanity.com/paper/2405.11389/) (2024)
- [Improved Convergence Analysis of Topology Dependence in Decentralized SGD](https://mlsanity.com/paper/2606.09154/) (2026)
- [Priority-Aware Learning-Unlearning Correction for Dynamic Decentralized LoRA Fine-Tuning](https://mlsanity.com/paper/2606.22878/) (2026)

## Abstract (arXiv)

In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy. We discover that the so-called expander graphs are near-optimal choices. We propose three approaches to construct expander graphs for different numbers of nodes and node degrees. Our numerical results show that the performance of decentralized optimization is significantly better on expander graphs than other regular graphs.