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

Breathe before speaking: efficient information dissemination despite noisy, limited and anonymous... 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 $$1/2-\epsilon $$ 1 / 2 - ϵ , for some small $$\epsilon >0$$ ϵ > 0 . Even in this severely restricted, stochastic and noisy setting we give natural protocols that solve the noisy broadcast and majority-consensus problems efficiently. Our protocols run in $$O(\log n/\epsilon ^2)$$ O ( log n / ϵ 2 ) rounds and use $$O(n \log n / \epsilon ^2)$$ O ( n log n / ϵ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Distributed Computing Springer Journals

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

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References (68)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer-Verlag Berlin Heidelberg
Subject
Computer Science; Computer Communication Networks; Computer Hardware; Computer Systems Organization and Communication Networks; Software Engineering/Programming and Operating Systems; Theory of Computation
ISSN
0178-2770
eISSN
1432-0452
DOI
10.1007/s00446-015-0249-4
Publisher site
See Article on Publisher Site

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 $$1/2-\epsilon $$ 1 / 2 - ϵ , for some small $$\epsilon >0$$ ϵ > 0 . Even in this severely restricted, stochastic and noisy setting we give natural protocols that solve the noisy broadcast and majority-consensus problems efficiently. Our protocols run in $$O(\log n/\epsilon ^2)$$ O ( log n / ϵ 2 ) rounds and use $$O(n \log n / \epsilon ^2)$$ O ( n log n / ϵ 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.

Journal

Distributed Computing – Springer Journals

Published: Jun 30, 2015

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