A discrete Benamou-Brenier formulation of Optimal Transport on graphs
Kieran Morris, Oliver Johnson
TL;DR
This paper introduces a discrete formulation of optimal transport on graphs, deriving a Benamou-Brenier analogue for Wasserstein-1 distance and classifying all geodesics.
Contribution
It develops a novel discrete transport equation on graphs and provides a new characterization of Wasserstein-1 geodesics in this setting.
Findings
Derived a discrete Benamou-Brenier formulation for Wasserstein-1 distance.
Classified all Wasserstein-1 geodesics on graphs.
Connected distributions on vertices and edges through a new transport equation.
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- distance on a graph and as a result classify all geodesics on graphs.
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