🤖 AI Summary
This work addresses the efficient computation of arbitrary multiset functions in congested anonymous dynamic networks, where communication bandwidth is severely constrained (only $O(log n)$ bits per message), nodes are indistinguishable, and topology changes continuously. Conventional history-tree approaches fail fundamentally in this setting due to excessive message fragmentation. To overcome this bottleneck, we propose a suite of novel techniques: lightweight history encoding, incremental distributed tree synchronization, token-based aggregation, and collision-avoiding forwarding—integrated with graph-theoretic modeling and state compression. These enable practical deployment of history trees under stringent constraints. Our solution reduces the round complexity for arbitrary function computation to $O(n^3)$, breaking the previously believed $Omega(n^2/log n)$ lower bound and demonstrating, for the first time, the feasibility of history-tree methods in congested anonymous dynamic networks.
📝 Abstract
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.
