The online joint replenishment problem (JRP) is a fundamental problem in the area of online problems with delay. Over the last decade, several works have studied generalizations of JRP with different cost functions for servicing requests. Most prior works on JRP and its generalizations have focused on the clairvoyant setting. Recently, Touitou [Tou23a] developed a non-clairvoyant framework that provided an $O(\sqrt{n \log n})$ upper bound for a wide class of generalized JRP, where $n$ is the number of request types. We advance the study of non-clairvoyant algorithms by providing a simpler, modular framework that matches the competitive ratio established by Touitou for the same class of generalized JRP. Our key insight is to leverage universal algorithms for Set Cover to approximate arbitrary monotone subadditive functions using a simple class of functions termed \textit{disjoint}. This allows us to reduce the problem to several independent instances of the TCP Acknowledgement problem, for which a simple 2-competitive non-clairvoyant algorithm is known. The modularity of our framework is a major advantage as it allows us to tailor the reduction to specific problems and obtain better competitive ratios. In particular, we obtain tight $O(\sqrt{n})$-competitive algorithms for two significant problems: Multi-Level Aggregation and Weighted Symmetric Subadditive Joint Replenishment. We also show that, in contrast, Touitou's algorithm is $\Omega(\sqrt{n \log n})$-competitive for both of these problems.

翻译：在线联合补货问题（JRP）是带延迟在线问题领域的一个基础性问题。过去十年间，多项研究探讨了具有不同服务请求成本函数的JRP推广形式。大多数关于JRP及其推广的研究集中于先知性设定。最近，Touitou [Tou23a] 提出了一个非先知性框架，为广义JRP的广泛类别提供了$O(\sqrt{n \log n})$的上界，其中$n$表示请求类型数量。我们通过构建一个更简洁、模块化的框架推进了非先知性算法的研究，该框架对同类广义JRP达到了与Touitou相同的竞争比。我们的核心洞见在于利用集合覆盖问题的通用算法，通过称为\textit{不相交}的简单函数类来逼近任意单调次可加函数。这使得我们可以将问题归约为多个独立的TCP确认问题实例，而该问题已知存在简单的2-竞争非先知性算法。我们框架的模块化特性具有显著优势，因为它允许针对特定问题定制归约方式并获得更优竞争比。特别地，我们为两个重要问题——多级聚合问题与加权对称次可加联合补货问题——给出了紧致的$O(\sqrt{n})$-竞争算法。同时我们证明，与此形成对比的是，Touitou算法对这两个问题的竞争比均为$\Omega(\sqrt{n \log n})$。