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Cooperative data exchange with priority classes

This paper considers the problem of cooperative data exchange with different client priority classes. In this problem, each client initially knows a subset of packets in the ground set X of size K, and all clients wish to learn all packets in X. The clients exchange packets by broadcasting coded combinations of their packets. The primary objective is to satisfy all high-priority clients in the first round of transmissions with minimum sum-rate, and the secondary objective is to satisfy low-priority clients in the second round of transmissions with minimum sum-rate, subject to minimizing the sum-rate in the first round. For any arbitrary problem instance, we provide a linear programming-based approach to find the minimum sum-rate in each round. Moreover, for the case in which the packets are randomly distributed among clients, we derive a closed-form expression for the minimum sum-rate in each round, which holds with probability approaching 1 as K tends to infinity.