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：匿名动态网络是一种由不可区分的进程组成的网络，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，在这些进程中，确定性计算给定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，其规模与进程数量成多项式关系。若网络拥塞，且仅能通过链路发送对数规模的消息，则此方法不可行。注意，由于进程的匿名性结合网络的动态性，将大型消息分多个轮次逐片发送本身并非解决方案。此外，已知某些基本任务（如全对全令牌分发，通过单令牌转发）在拥塞网络中需要Ω(n²/log n)轮次（Dutta 等，SODA 2013）。在本工作中，我们开发了一系列实用且高效的技术，使得在拥塞匿名动态网络中使用历史树成为可能。在其他应用中，我们展示了如何在O(n³)通信轮次内计算此类网络中的任意函数，大幅改进了先前针对拥塞网络的最先进算法。