Brief Announcement: Fast and Robust Information Spreading in the Noisy PULL Model

Boczkowski et al. (2018) considered the noisy PULL(h) model on the complete graph, where in each parallel round, every agent passively receives observations of the messages held by h randomly chosen agents, and where each message can be viewed as any other message in the alphabet ∑ with probability δ. The authors proved that in this model, the basic task of propagating a bit value from a single source to the whole population requires Ω(nδ/h(1-δ|∑|)2) rounds. The current work shows that the aforementioned lower bound is almost tight. We present two simple and efficient protocols that remain effective even in the presence of multiple conflicting sources, and quickly converge to their plurality opinion. Our first protocol operates with any alphabet of size at least two. Our second protocol, while slightly less efficient and requiring an alphabet of size four, is self-stabilizing. Overall, our results demonstrate how increasing the sample size can compensate for the lack of communication structure by linearly accelerating information spread.