  Optimal transport (OT) is a framework that can guide the design of efficient
resource allocation strategies in a network of multiple sources and targets. To
ease the computational complexity of large-scale transport design, we first
develop a distributed algorithm based on the alternating direction method of
multipliers (ADMM). However, such a distributed algorithm is vulnerable to
sensitive information leakage when an attacker intercepts the transport
decisions communicated between nodes during the distributed ADMM updates. To
this end, we propose a privacy-preserving distributed mechanism based on output
variable perturbation by adding appropriate randomness to each node's decision
before it is shared with other corresponding nodes at each update instance. We
show that the developed scheme is differentially private, which prevents the
adversary from inferring the node's confidential information even knowing the
transport decisions. Finally, we corroborate the effectiveness of the devised
algorithm through case studies.
