A discrete Benamou-Brenier formulation of Optimal Transport on graphs

• URL: http://arxiv.org/abs/2601.04193v1
• Date: Wed, 07 Jan 2026 18:59:07 GMT
• Title: A discrete Benamou-Brenier formulation of Optimal Transport on graphs
• Abstract summary: We 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.
• Score: 3.076702179889855
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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