  This paper considers the decentralized (discrete) optimal transport (D-OT)
problem. In this setting, a network of agents seeks to design a transportation
plan jointly, where the cost function is the sum of privately held costs for
each agent. We reformulate the D-OT problem as a constraint-coupled
optimization problem and propose a single-loop decentralized algorithm with an
iteration complexity of O(1/{\epsilon}) that matches existing centralized
first-order approaches. Moreover, we propose the decentralized equitable
optimal transport (DE-OT) problem. In DE-OT, in addition to cooperatively
designing a transportation plan that minimizes transportation costs, agents
seek to ensure equity in their individual costs. The iteration complexity of
the proposed method to solve DE-OT is also O(1/{\epsilon}). This rate improves
existing centralized algorithms, where the best iteration complexity obtained
is O(1/{\epsilon}^2).
