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Optimal Computation in Leaderless and Multi-Leader Disconnected 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

Giovanni Viglietta was partially funded by JSPS KAKENHI Grant number 23K10985.

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Giuseppe A. Di Luna and Giovanni Viglietta. Optimal Computation in Leaderless and Multi-Leader Disconnected Anonymous Dynamic Networks. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 18:1-18:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.DISC.2023.18

Abstract

We give a simple characterization of which functions can be computed deterministically by anonymous processes in dynamic networks, depending on the number of leaders in the network. In addition, we provide efficient distributed algorithms for computing all such functions assuming minimal or no knowledge about the network. Each of our algorithms comes in two versions: one that terminates with the correct output and a faster one that stabilizes on the correct output without explicit termination. Notably, these are the first deterministic algorithms whose running times scale linearly with both the number of processes and a parameter of the network which we call dynamic disconnectivity (meaning that our dynamic networks do not necessarily have to be connected at all times). We also provide matching lower bounds, showing that all our algorithms are asymptotically optimal for any fixed number of leaders. While most of the existing literature on anonymous dynamic networks relies on classical mass-distribution techniques, our work makes use of a recently introduced combinatorial structure called history tree, also developing its theory in new directions. Among other contributions, our results make definitive progress on two popular fundamental problems for anonymous dynamic networks: leaderless Average Consensus (i.e., computing the mean value of input numbers distributed among the processes) and multi-leader Counting (i.e., determining the exact number of processes in the network). In fact, our approach unifies and improves upon several independent lines of research on anonymous networks, including Nedić et al., IEEE Trans. Automat. Contr. 2009; Olshevsky, SIAM J. Control Optim. 2017; Kowalski-Mosteiro, ICALP 2019, SPAA 2021; Di Luna-Viglietta, FOCS 2022.

Subject Classification

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

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