Rate Allocation and Content Placement in Cache Networks

TL;DR

This paper addresses the joint optimization of rate allocation and content placement in cache networks, proposing algorithms with provable optimality guarantees for a complex non-convex problem involving DR-submodular functions.

Contribution

It introduces a novel formulation for congestion control in cache networks and develops two algorithms with theoretical guarantees for solving the non-convex optimization problem.

Findings

Lagrangian barrier algorithm achieves certain optimality guarantees.

Convex relaxation provides alternative solutions with different guarantees.

The problem involves non-convex constraints related to DR-submodular functions.

Abstract

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.