An anonymous dynamic network is a network of indistinguishable processes whose communication links may appear or disappear unpredictably over time. Previous research has shown that deterministically computing an arbitrary function of a multiset of input values given to these processes takes only a linear number of communication rounds (Di Luna-Viglietta, FOCS 2022). However, fast algorithms for anonymous dynamic networks rely on the construction and transmission of large data structures called "history trees", whose size is polynomial in the number of processes. This approach is unfeasible if the network is congested, and only messages of logarithmic size can be sent through its links. Observe that sending a large message piece by piece over several rounds is not in itself a solution, due to the anonymity of the processes combined with the dynamic nature of the network. Moreover, it is known that certain basic tasks such as all-to-all token dissemination (by means of single-token forwarding) require $\Omega(n^2/\log n)$ rounds in congested networks (Dutta et al., SODA 2013). In this work, we develop a series of practical and efficient techniques that make it possible to use history trees in congested anonymous dynamic networks. Among other applications, we show how to compute arbitrary functions in such networks in $O(n^3)$ communication rounds, greatly improving upon previous state-of-the-art algorithms for congested networks.

翻译：匿名动态网络是由不可区分的进程构成的网络，其通信链路可能随时间不可预测地出现或消失。先前的研究表明，确定性计算这些进程所接收输入值多重集的任意函数仅需线性数量的通信轮次（Di Luna-Viglietta, FOCS 2022）。然而，匿名动态网络的快速算法依赖于构建和传输称为"历史树"的大型数据结构，其大小与进程数量呈多项式关系。若网络处于拥塞状态且链路仅能传输对数规模的消息，该方法则不可行。需注意，由于进程的匿名性与网络的动态性相结合，将大消息分片在多轮中发送本身并非解决方案。此外，已知某些基本任务（例如通过单令牌转发的全对全令牌传播）在拥塞网络中需要 $\Omega(n^2/\log n)$ 轮次（Dutta et al., SODA 2013）。本工作开发了一系列实用高效的技术，使得在拥塞匿名动态网络中使用历史树成为可能。除其他应用外，我们展示了在此类网络中如何以 $O(n^3)$ 通信轮次计算任意函数，显著改进了先前针对拥塞网络的最先进算法。