Efficient and distributed computation of maximum multicast rates

The transmission of information within a data network is constrained by network topology and link capacities. In this paper, we study the fundamental upper bound of information multicast rates with these constraints, given the unique replicable and encodable property of information flows. Based on recent information theory advances in coded multicast rates, we are able to formulate the maximum multicast rate problem as a linear network optimization problem, assuming the general undirected network model. We then proceed to apply Lagrangian relaxation techniques to obtain (1) a necessary and sufficient condition for multicast rate feasibility, and (2) a subgradient solution for computing the maximum rate and the optimal routing strategy to achieve it. The condition we give is a generalization of the well-known conditions for the unicast and broadcast cases. Our subgradient solution takes advantage of the underlying network flow structure of the problem, and therefore outperforms general linear programming solving techniques. It also admits a natural intuitive interpretation, and is amenable to fully distributed implementations.