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.

翻译：我们在缓存网络中引入了最佳拥堵控制问题, 从而优化比例分配和内容配置。 我们将此作为非隐形限制的最大化问题, 并提议通过(a) Lagrangian 屏障算法和(b) convex 放松来解决这个问题。 我们证明这两种算法都存在不同的最佳保障; 我们的证据利用了这样一个事实,即我们问题的非隐形限制涉及DR- 子模块功能。