We introduce the problem of optimal congestion control in cache networks, whereby \emph{both} rate allocations and content placements are optimized \emph{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.
@article{arxiv.2101.03441,
title = {Rate Allocation and Content Placement in Cache Networks},
author = {Khashayar Kamran and Armin Moharrer and Stratis Ioannidis and Edmund Yeh},
journal= {arXiv preprint arXiv:2101.03441},
year = {2021}
}