An Approximation Algorithm for Optimal Clique Cover Delivery in Coded Caching

TL;DR

This paper introduces an approximation algorithm for the clique cover delivery problem in coded caching, reducing bandwidth more effectively than existing methods, especially with arbitrary user content placement.

Contribution

It formulates the clique cover delivery as a combinatorial optimization problem and proposes a $(1 + ext{log} K)$ approximation algorithm, improving over previous linear-ratio schemes.

Findings

The algorithm achieves a $(1 + ext{log} K)$ approximation ratio.

Numerical results show significant bandwidth reduction.

The approach outperforms existing schemes in most scenarios.

Abstract

Coded caching can significantly reduce the communication bandwidth requirement for satisfying users' demands by utilizing the multicasting gain among multiple users. Most existing works assume that the users follow the prescriptions for content placement made by the system. However, users may prefer to decide what files to cache. To address this issue, we consider a network consisting of a file server connected through a shared link to $K$ users, each equipped with a cache which has been already filled arbitrarily. Given an arbitrary content placement, the goal is to find a delivery strategy for the server that minimizes the load of the shared link. In this paper, we focus on a specific class of coded multicasting delivery schemes known as the "clique cover delivery scheme". We first formulate the optimal clique cover delivery problem as a combinatorial optimization problem. Using a connection with the weighted set cover problem, we propose an approximation algorithm and show that it provides an approximation ratio of $(1 + \log K)$, while the approximation ratio for the existing coded delivery schemes is linear in $K$. Numerical simulations show that our proposed algorithm provides a considerable bandwidth reduction over the existing coded delivery schemes for almost all content placement schemes.