This paper studies the multi-access coded caching (MACC) problem under arbitrary user-cache access topologies, extending existing models that rely on highly structured and combinatorially designed connectivity. We consider a MACC system consisting of a single server, multiple cache nodes, and multiple user nodes. Each user can access an arbitrary subset of cache nodes to retrieve cached content. The objective is to design a general and low-complexity delivery scheme under fixed cache placement for arbitrary access topologies. We propose a universal graph-based framework for modeling the MACC delivery problem, where decoding conflicts among requested packets are captured by a conflict graph and the delivery design is reduced to a graph coloring problem. In this formulation, a lower transmission load corresponds to using fewer colors. The classical greedy coloring algorithm DSatur achieves a transmission load close to the index-coding converse bound, providing a tight benchmark, but its computational complexity becomes prohibitive for large-scale graphs. To overcome this limitation, we develop a learning-based framework using graph neural networks that efficiently constructs near-optimal coded multicast transmissions and generalizes across diverse access topologies and varying numbers of users. In addition, we extend the index-coding converse bound for uncoded cache placement to arbitrary access topologies and propose a low-complexity greedy approximation. Numerical results demonstrate that the proposed learning-based scheme achieves transmission loads close to those of DSatur and the converse bound while significantly reducing computational time.

翻译：本文研究了任意用户-缓存接入拓扑下的多址编码缓存问题，拓展了现有依赖高度结构化组合设计连接性的模型。我们考虑一个由单个服务器、多个缓存节点和多个用户节点组成的多址编码缓存系统。每个用户可访问任意缓存节点子集以获取缓存内容。目标是在固定缓存放置条件下，为任意接入拓扑设计一种通用且低复杂度的内容传输方案。我们提出了一种基于图的通用框架来建模多址编码缓存传输问题，其中请求数据包间的解码冲突通过冲突图刻画，传输设计被转化为图着色问题。在此框架下，较低的传输负载对应于使用更少的颜色数。经典贪心着色算法DSatur能达到接近索引编码逆界的传输负载，提供了紧致的性能基准，但其计算复杂度在大规模图场景下将变得不可承受。为克服该限制，我们开发了一种基于图神经网络的学习框架，能高效构建近似最优的编码组播传输，并泛化至多样化的接入拓扑和用户规模。此外，我们将未编码缓存放置下的索引编码逆界推广至任意接入拓扑，并提出一种低复杂度贪心近似算法。数值结果表明，所提出的学习方案在显著降低计算时间的同时，实现了接近DSatur算法和逆界的传输负载。