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What Can Be Computed in Average Anonymous Networks?

Authors Joel Rybicki , Oleg Verbitsky , Maksim Zhukovskii

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ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • Average-case complexity
  • anonymous networks
  • unique identifiers
  • triangle finding
  • random graphs
  • color refinement

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Abstract

We study deterministic distributed algorithms on random input graphs. We show that an extremely weak anonymous model of distributed computing can efficiently simulate the standard LOCAL and broadcast CONGEST models with high probability on random input graphs. In this weak model, all nodes are anonymous, and in each communication round, nodes broadcast a message to all their neighbors, receive an unordered set of messages from their neighbors, and update their local state. This is the SB model introduced by Hella et al. [PODC 2012], which is strictly weaker than the standard port-numbering PN model.
Specifically, we give a one-round deterministic SB-algorithm using O(log n)-bit messages that computes unique O(log n)-bit identifiers with high probability on anonymous networks sampled from G(n,p), where n^{ε-1} ≤ p ≤ 1/2 and ε > 0 is an arbitrarily small constant. Inspired by canonical labeling techniques in graph isomorphism testing, this construction allows existing distributed algorithms designed for the broadcast CONGEST and LOCAL models to be simulated in anonymous networks with only a small overhead. As a further application of our "anonymization" approach, we give a new algorithm for finding a triangle in O(1/ε) rounds on G(n,p) for p as above.
We also investigate the computational power of natural analogs of "Monte Carlo" and "Las Vegas" distributed graph algorithms in the random graph setting, and establish collapse and hierarchy results for both types of algorithms.

Cite As Get BibTex

Joel Rybicki, Oleg Verbitsky, and Maksim Zhukovskii. What Can Be Computed in Average Anonymous Networks?. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 40:1-40:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.DISC.2026.40

Author Details

Joel Rybicki
  • Humboldt-Universität zu Berlin, Germany
Oleg Verbitsky
  • Humboldt-Universität zu Berlin, Germany
Maksim Zhukovskii
  • School of Computer Science, University of Sheffield, UK

Funding

  • Verbitsky, Oleg: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – project number 572124308. On leave from the IAPMM, Lviv, Ukraine.

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