This paper studies the multi-access coded caching (MACC) problem with arbitrary user-cache access topology, which extends existing MACC models that rely on highly structured and combinatorially designed topologies. We consider a MACC system consisting of a single server, $Λ$ cache-nodes, and $K$ user-nodes. The server stores $N$ equal-size files, each cache-node has a storage capacity of $M$ files, and each user-node $k\in[K]$ can access an arbitrary subset of cache-nodes $\mathcal{A}_k\subseteq[Λ]$ and retrieve the cached content stored in cache-nodes $\mathcal{A}_k$. The objective is to design a universal framework for the MACC delivery problem. Decoding conflicts among the requested packets are captured by a conflict graph, and the design of the delivery is reduced to a graph coloring problem, where achieving a lower transmission load corresponds to coloring the graph using fewer colors. Under this formulation, the classical DSatur algorithm achieves a transmission load close to the index-coding (IC) converse bound, thereby providing a practical benchmark. However, its computational complexity becomes prohibitive for large-scale graphs. To overcome this limitation, we develop a learning-driven approach using graph neural networks (GNNs) that efficiently constructs coded multicast transmissions with performance close to the theoretical bounds and generalizes across different user-cache access topologies and numbers of users. In addition, we extend the IC converse bound to MACC systems with arbitrary access topology and propose a low-complexity greedy approximation that closely matches the IC converse bound. Numerical results demonstrate that the proposed approach achieves performance close to the DSatur algorithm and the IC converse bound, while significantly reducing computational complexity, making it well-suited for large-scale MACC systems.

翻译：本文研究了具有任意用户缓存访问拓扑的多接入编码缓存（MACC）问题，该问题扩展了现有依赖高度结构化及组合设计拓扑的MACC模型。我们考虑一个包含单个服务器、$\Lambda$个缓存节点和$K$个用户节点的MACC系统。服务器存储$N$个等大小文件，每个缓存节点拥有$M$个文件的存储容量，且每个用户节点$k\in[K]$可访问任意缓存节点子集$\mathcal{A}_k\subseteq[\Lambda]$并检索存储在$\mathcal{A}_k$中的缓存内容。目标是设计一个通用的MACC交付问题框架。请求数据包间的解码冲突由冲突图捕获，交付设计简化为图着色问题，其中更低的传输负载对应使用更少颜色为图着色。在此框架下，经典DSatur算法实现的传输负载接近索引编码（IC）逆界，从而提供了实用基准。然而，其计算复杂度在大规模图中变得难以承受。为克服此限制，我们开发了一种基于图神经网络（GNN）的学习驱动方法，该方法能高效构造编码多播传输，性能接近理论界，并可推广至不同用户缓存访问拓扑及用户数量。此外，我们将IC逆界扩展到任意访问拓扑的MACC系统中，并提出一种低复杂度贪心近似方法，其性能与IC逆界紧密匹配。数值结果表明，所提方法在显著降低计算复杂度的同时，性能接近DSatur算法与IC逆界，使其特别适用于大规模MACC系统。