What can be computed in average anonymous networks?

A team of computer scientists—Joel Rybicki, Oleg Verbitsky, and Maksim Zhukovskii—has published a breakthrough paper investigating what can be computed in 'average anonymous networks.' They focus on extremely weak distributed computing models where nodes have no identifiers (anonymous) and can only broadcast to neighbors and receive multisets of messages each round. These are the SB and MB models, which are strictly weaker than standard port-numbering (PN) and LOCAL models used in most distributed algorithms research.

Their key innovation is a one-round deterministic SB-algorithm that uses O(log n)-bit messages to compute unique identifiers with high probability on anonymous networks sampled from G(n,p), where n^(ε-1) ≤ p ≤ 1/2 and ε > 0 is a small constant. Inspired by canonical labeling techniques from graph isomorphism testing, this algorithm effectively 'anonymizes' existing distributed graph algorithms designed for the broadcast CONGEST and LOCAL models. For example, they demonstrate a new anonymous algorithm that finds a triangle in O(1/ε) rounds on the same input distribution.

The research also investigates computational power analogs of 'Monte Carlo' and 'Las Vegas' distributed algorithms in random graph settings, establishing new collapse and hierarchy results. Most significantly, their work shows the collapse of the weak model hierarchy proposed by Hella et al. on G(n,p)—apart from a vanishingly small fraction of input graphs, the SB model proves to be as powerful as the much stronger LOCAL model. This 34-page paper, submitted to arXiv in April 2026, represents a fundamental advance in understanding the limits of computation in anonymous distributed systems.