Fast and Robust Information Spreading in the Noisy PULL Model

Efficient information spreading in stochastic multi-agent systems is a core challenge when communication is noisy, bandwidth-limited, and agents lack global coordination. Yet biological systems-such as ant colonies and fish schools-routinely overcome these constraints: a small number of informed individuals can reliably guide large, uncoordinated populations using minimal, noisy signals. Motivated by these observations, we investigate how reliable information dissemination can be achieved in bio-inspired stochastic settings with limited communication and no global control. We analyze the noisy PULL(ℎ) model, covering a general setting that spans from rumor spreading to majority consensus: a subset of source agents hold initial preferences, and the goal is to converge to the majority preference. Agents passively observe noisy messages from ℎ randomly sampled peers per round. Prior work shows that convergence requires Ω(n/ℎ) rounds even under favorable conditions. We ask: how far can one push simplicity-no synchronization and minimal message size-without compromising convergence speed? We present a quasi self-stabilizing protocol using only 2-bit messages that converges from arbitrary initial states despite severe noise and asynchrony. It achieves optimal convergence time O((n/ℎ) logn) with high probability, and O(logn) time in the fully connected case ℎ = n. A key subroutine is an even simpler 1-bit protocol assuming simultaneous start, based on a natural two-phase “listen-then-amplify” mechanism reminiscent of biological strategies. Together, our results connect biologically inspired heuristics with provable guarantees for robust, efficient information dissemination in highly unreliable and uncoordinated systems.