We investigate the problem of coded caching for nonuniform demands when the structured clique cover algorithm proposed by Maddah-Ali and Niesen for decentralized caching is used for delivery. We apply this algorithm to all user demands regardless of their request probabilities. This allows for coding among the files that have different request probabilities but makes the allocation of memory to different files challenging during the content placement phase. As our main contribution, we analytically characterize the optimal placement strategy that minimizes the expected delivery rate under a storage capacity constraint. It is shown that the optimal placement follows either a two or a three group strategy, where a set of less popular files are not cached at all and the files within each of the other sets are allocated identical amounts of storage as if they had the same request probabilities. We show that for a finite set of storage capacities, that we call the base-cases of the problem, the two group strategy is always optimal. For other storage capacities, optimal placement is achieved by memory sharing between certain base-cases and the resulting placement either follows a two or a three group strategy depending on the corresponding base-cases used. We derive a polynomial time algorithm that determines the base-cases of the problem given the number of caches and popularity distribution of files. Given the base-cases of the problem, the optimal memory allocation parameters for any storage capacity are derived analytically.

中文翻译：

---

非均匀需求的结构化集团覆盖交付的最佳未编码位置的完整表征

我们研究了当 Maddah-Ali 和 Niesen 提出的用于分散缓存的结构化集团覆盖算法用于交付时，针对非均匀需求的编码缓存问题。我们将此算法应用于所有用户需求，而不管他们的请求概率如何。这允许在具有不同请求概率的文件之间进行编码，但使得在内容放置阶段将内存分配到不同文件具有挑战性。作为我们的主要贡献，我们分析了在存储容量限制下最小化预期交付率的最佳放置策略的特征。结果表明，最佳放置遵循二组或三组策略，其中一组不太流行的文件根本没有被缓存，并且每个其他组中的文件都被分配了相同数量的存储空间，就好像它们具有相同的请求概率一样。我们表明，对于有限的一组存储容量，我们称之为问题的基本情况，两组策略总是最优的。对于其他存储容量，通过某些基本案例之间的内存共享来实现最佳放置，并且根据所使用的相应基本案例，最终放置遵循二组或三组策略。我们推导出多项式时间算法，该算法在给定缓存数量和文件流行度分布的情况下确定问题的基本情况。给定问题的基本情况，分析导出任何存储容量的最佳内存分配参数。