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Efficient Computation in Congested Anonymous Dynamic Networks

Authors Giuseppe A. Di Luna, Giovanni Viglietta

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Author Details

Giuseppe A. Di Luna
  • DIAG, Sapienza University of Rome, Italy
Giovanni Viglietta
  • Department of Computer Science and Engineering, University of Aizu, Japan

Funding

Giuseppe A. Di Luna was Giovanni Viglietta was
  • Di Luna, Giuseppe A.: partially supported by Sapienza Progetto Ateneo RM1221816C1760BF.
  • Viglietta, Giovanni: partially supported by the JSPS KAKENHI grant 23K10985.

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Giuseppe A. Di Luna and Giovanni Viglietta. Efficient Computation in Congested Anonymous Dynamic Networks. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 49:1-49:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.MFCS.2024.49

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 Ω(n²/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(n³) communication rounds, greatly improving upon previous state-of-the-art algorithms for congested networks.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Computing methodologies → Distributed algorithms
Keywords
  • anonymous dynamic network
  • congested network
  • history tree

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