Rate Allocation and Content Placement in Cache Networks

We introduce the problem of optimal congestion control in cache networks, whereby both rate allocations and content placements are optimized jointly. We formulate this as a maximization problem with non-convex constraints, and propose solving this problem via (a) a Lagrangian barrier algorithm and (b) a convex relaxation. We prove different optimality guarantees for each of these two algorithms; our proofs exploit the fact that the non-convex constraints of our problem involve DR-submodular functions.