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Broadcasts in Anonymous, Dynamic Networks: A New Algorithm and Impossibility Results

Author Volker Turau

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LIPIcs.SAND.2026.6.pdf
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  • 17 pages

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Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Graph algorithms analysis
Keywords
  • Distributed algorithms
  • dynamic networks
  • randomized algorithms
  • impossibility results

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Abstract

The broadcast problem is the task of disseminating a message from a single source node to all other nodes in a distributed system, ensuring that every node eventually receives the message despite possible network constraints such as delays, failures, or limited topology knowledge. In this work, we consider the broadcast problem in anonymous, synchronous, dynamic networks. A dynamic network is a network, whose topology changes over time, meaning that communication links can unpredictably appear and disappear. We present a randomized algorithm requiring O(log log n) bits of storage per node and terminating in O(m log n) rounds with high probability. It solves broadcast with stabilizing termination for anonymous, synchronous, 1-interval-connected networks using messages of size O(1). The algorithm is a non-idle-start algorithm. The best known idle-start algorithm for this problem requires O(log n) space, also a lower memory bound of ω(1) space is known. Our contribution affirmatively answers a question of Parzych and Daymude (DISC 2024). We also extend this result to dynamic networks with bounded connectivity time. Furthermore, we prove that for two variants of the broadcast problem in this setting no randomized algorithms exist.

Cite As Get BibTex

Volker Turau. Broadcasts in Anonymous, Dynamic Networks: A New Algorithm and Impossibility Results. In 5th Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 373, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.SAND.2026.6

Author Details

Volker Turau
  • Hamburg University of Technology, Germany

References

  1. Ran Ben Basat, Keren Censor-Hillel, Yi-Jun Chang, Wenchen Han, Dean Leitersdorf, and Gregory Schwartzman. Bounded memory in distributed networks. In Proc. of the 37th ACM Symposium on Parallelism in Algorithms and Architectures, pages 566-581, 2025. URL: https://doi.org/10.1145/3694906.3743302.
  2. Lucas Boczkowski, Amos Korman, and Emanuele Natale. Minimizing message size in stochastic communication patterns: Fast self-stabilizing protocols with 3 bits. In Proc. 2017 Annual ACM-SIAM Symp. on Discrete Algo. (SODA), pages 2540-2559, 2017. URL: https://doi.org/10.1137/1.9781611974782.168.
  3. Arnaud Casteigts, Paola Flocchini, Bernard Mans, and Nicola Santoro. Deterministic computations in time-varying graphs: Broadcasting under unstructured mobility. In IFIP Int. Conference on Theoretical Computer Science, pages 111-124. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-15240-5_9.
  4. Arnaud Casteigts, Paola Flocchini, Bernard Mans, and Nicola Santoro. Shortest, fastest, and foremost broadcast in dynamic networks. Int. Journal of Foundations of Computer Science, 26(4):499-522, 2015. URL: https://doi.org/10.1142/S0129054115500288.
  5. Arnaud Casteigts, Paola Flocchini, Walter Quattrociocchi, and Nicola Santoro. Time-varying graphs and dynamic networks. Int. Journal of Parallel, Emergent and Distributed Systems, 27(5):387-408, 2012. URL: https://doi.org/10.1080/17445760.2012.668546.
  6. Robert M. Corless, Gaston H. Gonnet, David E. G. Hare, David J. Jeffrey, and Donald E. Knuth. On the Lambert W Function. Advances in Computational Mathematics, 5(1):329-359, 1996. URL: https://doi.org/10.1007/BF02124750.
  7. Giuseppe A Di Luna and Giovanni Viglietta. Optimal computation in leaderless and multi-leader disconnected anonymous dynamic networks. In 37^th Int. Symp. on Distr. Comp. (DISC), pages 18-1. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2023. URL: https://doi.org/10.4230/LIPIcs.DISC.2023.18.
  8. Giuseppe A Di Luna and Giovanni Viglietta. Efficient computation in congested anonymous dynamic networks. Distributed Computing, pages 1-18, 2025. URL: https://doi.org/10.1007/s00446-025-00481-z.
  9. Philippe Flajolet. Approximate counting: a detailed analysis. BIT Numerical Mathematics, 25(1):113-134, 1985. URL: https://doi.org/10.1007/BF01934993.
  10. Walter Hussak and Amitabh Trehan. Termination of amnesiac flooding. Distributed Computing, 36(2):193-207, 2023. URL: https://doi.org/10.1007/S00446-023-00448-Y.
  11. Amos Korman and Robin Vacus. Early adapting to trends: self-stabilizing information spread using passive communication. Distributed Computing, 37(4):335-362, 2024. URL: https://doi.org/10.1007/S00446-024-00462-8.
  12. Dariusz R. Kowalski and Miguel A. Mosteiro. Anonymous adversarial dynamic networks with logarithmic memory and communication. Theoretical Computer Science, 1066:115740, 2026. URL: https://doi.org/10.1016/j.tcs.2025.115740.
  13. Fabian Kuhn, Nancy A. Lynch, and Rotem Oshman. Distributed computation in dynamic networks. In Leonard J. Schulman, editor, Proc. 42^nd ACM Symp. on Theory of Computing, STOC, pages 513-522. ACM, 2010. URL: https://doi.org/10.1145/1806689.1806760.
  14. Othon Michail, Ioannis Chatzigiannakis, and Paul G Spirakis. Causality, influence, and computation in possibly disconnected synchronous dynamic networks. Journal of Parallel and Distributed Computing, 74(1):2016-2026, 2014. URL: https://doi.org/10.1016/J.JPDC.2013.07.007.
  15. Robert Morris. Counting large numbers of events in small registers. Communications of the ACM, 21(10):840-842, 1978. URL: https://doi.org/10.1145/359619.359627.
  16. Jelani Nelson and Huacheng Yu. Optimal bounds for approximate counting. In Proc. of the 41^st ACM SIGMOD-SIGACT-SIGAI Symp. on Principles of Database Systems, pages 119-127, 2022. URL: https://doi.org/10.1145/3517804.3526225.
  17. Garrett Parzych and Joshua J. Daymude. Memory lower bounds and impossibility results for anonymous dynamic broadcast. In Dan Alistarh, editor, 38^th Int. Symp. on Distr. Comp. DISC, volume 319 of LIPIcs, pages 35:1-35:18, 2024. URL: https://doi.org/10.4230/LIPIcs.DISC.2024.35.
  18. Michel Raynal, Julien Stainer, Jiannong Cao, and Weigang Wu. A simple broadcast algorithm for recurrent dynamic systems. In 2014 IEEE 28th International Conference on Advanced Information Networking and Applications, pages 933-939. IEEE, 2014. URL: https://doi.org/10.1109/AINA.2014.115.
  19. Volker Turau. Synchronous concurrent broadcasts for intermittent channels with bounded capacities. In Tomasz Jurdzinski and Stefan Schmid, editors, Struc. Inf. and Com. Complexity - 28^th SIROCCO, volume 12810 of LNCS, pages 296-312. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-79527-6_17.
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