Breathe before speaking: efficient information dissemination despite noisy, limited and anonymous communication

Abstract

Distributed computing models typically assume reliable communication between processors. While such assumptions often hold for engineered networks, e.g., due to underlying error correction protocols, their relevance to biological systems, wherein messages are often distorted before reaching their destination, is quite limited. In this study we take a first step towards reducing this gap by rigorously analyzing a model of communication in large anonymous populations composed of simple agents which interact through short and highly unreliable messages.We focus on the broadcast problem and the majority-consensus problem. Both are fundamental information dissemination problems in distributed computing, in which the goal of agents is to converge to some prescribed desired opinion. We initiate the study of these problems in the presence of communication noise. Our model for communication is extremely weak and follows the push gossip communication paradigm: In each round each agent that wishes to send information delivers a message to a random anonymous agent. This communication is further restricted to contain only one bit (essentially representing an opinion). Lastly, the system is assumed to be so noisy that the bit in each message sent is flipped independently with probability 1/2 − ǫ, for some small ǫ > 0.Even in this severely restricted, stochastic and noisy setting we give natural protocols that solve the noisy broadcast and the noisy majority-consensus problems efficiently. Our protocols run in O(log n/ǫ 2 ) rounds and use O(n log n/ǫ 2 ) messages/bits in total, where n is the number of agents. These bounds are asymptotically optimal and, in fact, are as fast and message efficient as if each agent would have been simultaneously informed directly by an agent that knows the prescribed desired opinion. Our efficient, robust, and simple algorithms suggest balancing between silence and transmission, synchronization, and majority-based decisions as important ingredients towards understanding collective communication schemes in anonymous and noisy populations.

Noisy rumor spreading and plurality consensus

“…Thanks to the achievements of this theory, the impact of noise can often be drastically reduced to almost zero by employing error-correcting codes, which are practical methods whenever dealing with artificial entities. However, as observed in [26], the situation is radically different for scenarios in which the computational entities are biological. Indeed, from a biological perspective, a computational process can be considered "simple" only if it consists of very basic primitive operations, and is extremely lightweight.…”

“…An important step toward understanding communications in biological ensembles has been achieved recently in [26], which showed how it is possible to cope with noisy communications in absence of coding mechanisms for solving complex tasks such as rumor-spreading and majority consensus. Such a result provides highly valuable hints on how complex tasks can be achieved in frameworks such as the immune system, bacteria populations, or superorganisms of social insects, despite the presence of noisy communications.…”

“…In the case of rumor-spreading, [26] assumes that a sourcenode initially handles a bit, set to some binary value, called the correct opinion. This opinion has to be transmitted to all nodes, in a noisy environment, modeled as a complete network with unreliable links.…”

“…It is proved that, even in this very noisy setting, the rumor-spreading problem can be solved quite efficiently. Specifically, [26] provides an algorithm that solves the noisy rumor-spreading problem in O( 1 2 log n) communication rounds, with high probability 1 (w.h.p.) in n-node networks, using O(log log n + log(1/ )) bits of memory per node 2 .…”

“…In the case of majority consensus, [26] assumes that some nodes are supporting opinion 0, some nodes are supporting opinion 1, and some other nodes are supporting no opinion. The objective is that all nodes eventually support the initially most frequent opinion (0 or 1).…”