Fast and Robust Information Spreading in the Noisy PULL Model : Extended Abstract
Résumé
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(?/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 se- vere noise and asynchrony. It achieves optimal convergence time ? ((?/ℎ) log ?) with high probability, and ? (log ?) time in the fully connected case ℎ = ?. 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 strate- gies. Together, our results connect biologically inspired heuristics with provable guarantees for robust, efficient information dissemi- nation in highly unreliable and uncoordinated systems.
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