A discrete Benamou-Brenier formulation of Optimal Transport on graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913034347216896 |
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| author | Morris, Kieran Johnson, Oliver |
| author_facet | Morris, Kieran Johnson, Oliver |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_04193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A discrete Benamou-Brenier formulation of Optimal Transport on graphs Morris, Kieran Johnson, Oliver Information Theory Probability Machine Learning 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. |
| title | A discrete Benamou-Brenier formulation of Optimal Transport on graphs |
| topic | Information Theory Probability Machine Learning |
| url | https://arxiv.org/abs/2601.04193 |