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A discrete Benamou-Brenier formulation of Optimal Transport on graphs
Published 7 Jan 2026 in cs.IT, math.PR, and stat.ML | (2601.04193v1)
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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