Efficient Computation in Congested Anonymous Dynamic Networks

TL;DR

This paper introduces new techniques enabling efficient computation of arbitrary functions in congested anonymous dynamic networks, significantly reducing communication rounds compared to previous methods that relied on large data structures.

Contribution

The authors develop practical techniques that adapt history trees for use in congested anonymous dynamic networks, enabling faster computation of functions.

Findings

Achieved $O(n^3)$ rounds for arbitrary function computation in congested networks.

Improved upon previous algorithms that required more rounds or were infeasible due to congestion.

Demonstrated practical applicability of history trees in highly dynamic, bandwidth-limited environments.

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.