# Distributed Computation of Wasserstein Barycenters over Networks

arXiv: https://arxiv.org/abs/1803.02933 · HTML: https://mlsanity.com/paper/1803.02933/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2018.

## Built on by (most cited first, 5 of 5)

- [An Accelerated Stochastic Variance-Reduced Algorithm for Entropic Wasserstein Barycenters](https://mlsanity.com/paper/2203.00813/) (2022)
- [First-Order Methods for Convex Optimization](https://mlsanity.com/paper/2101.00935/) (2021)
- [FLECS-CGD: A Federated Learning Second-Order Framework via Compression and Sketching with Compressed Gradient Differences](https://mlsanity.com/paper/2210.09626/) (2022)
- [Decentralized Entropic Optimal Transport for Distributed Distribution Comparison](https://mlsanity.com/paper/2301.12065/) (2023)
- [Field Codes for Distributed Coupling Samplers and Certified Empirical Transport](https://mlsanity.com/paper/2607.27078/) (2026)

## Abstract (arXiv)

We propose a new cuclass-optimal algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of all distributions held in the network by using local interactions compliant with the topology of the graph. We provide an estimate for the minimum number of communication rounds required for the proposed method to achieve arbitrary relative precision both in the optimality of the solution and the consensus among all agents for undirected fixed networks.