  Optimal transport has been used extensively in resource matching to promote
the efficiency of resources usages by matching sources to targets. However, it
requires a significant amount of computations and storage spaces for
large-scale problems. In this paper, we take a consensus-based approach to
decentralize discrete optimal transport problems and develop fully distributed
algorithms with alternating direction method of multipliers. We show that our
algorithms guarantee certain levels of efficiency and privacy besides the
distributed nature. We further derive primal and dual algorithms by exploring
the primal and dual problems of discrete optimal transport with linear utility
functions and prove the equivalence between them. We verify the convergence,
online adaptability, and the equivalence between the primal algorithm and the
dual algorithm with numerical experiments. Our algorithms reflect the
bargaining between sources and targets on the amounts and prices of transferred
resources and reveal an averaging principle which can be used to regulate
resource markets and improve resource efficiency.
