A discrete Benamou-Brenier formulation of Optimal Transport on graphs
arXiv:2601.0419312.3h-index: 3
AI Analysis
This provides a theoretical foundation for optimal transport on graphs, relevant for researchers in graph-based machine learning and network analysis.
The authors propose a discrete transport equation on graphs and derive a discrete analogue of the Benamou-Brenier formulation for the Wasserstein-1 distance, classifying all W1 geodesics on graphs.
We propose a discrete transport equation on graphs which connects distributions on both vertices and edges. We then derive a discrete analogue of the Benamou-Brenier formulation for Wasserstein-$1$ distance on a graph and as a result classify all $W_1$ geodesics on graphs.