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

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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 \(1/2-\epsilon \), for some small \(\epsilon >0\). 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 \(O(\log n/\epsilon ^2)\) rounds and use \(O(n \log n / \epsilon ^2)\) 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.

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Notes

  1. Network information theory [31] discusses the problem of disseminating information from one or more sources to a large number of recipients over noisy information channels. The settings there are, however, different from those that interest us as they are non-distributed in nature and allow for complex coding schemes that may be computationally complex for simple agents [41].

  2. One could view this trait as a consequence of a symmetry of the world, in which an agent can decide if two opinions are the same or not but has no access to their actual values. For example, a flock of birds following a source (e.g., a bird that has spotted a predator) that travels either north or south can do this even in an environment where there is complete symmetry between these two directions. The only demand is that the escape direction of all birds agree with that of the source.

  3. Specifically, in Stage 1, an agent activated in phase i, chooses a single message uniformly at random among the messages it has received in phase i and sets its initial opinion to the content of that message. In Stage 2, at the end of each phase i, a successful agent selects a subset of samples of size \(m_i/2\) uniformly at random among the set of samples it has received in that phase, and then update its opinion to be the majority opinion in that subset.

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Acknowledgments

The authors would like to thank Oded Goldreich, Kunal Talwar, James Aspnes, and George Giakkoupis for helpful discussions.

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Authors and Affiliations

  1. The Shlomo and Michla Tomarin Career Development Chair, Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot, Israel

    Ofer Feinerman

  2. School of Computer Science, Carnegie Mellon University, Pittsburgh, PA, USA

    Bernhard Haeupler

  3. The Laboratory of Computer Algorithms: Fundamentals and Applications (LIAFA), CNRS, University Paris Diderot, Paris, France

    Amos Korman

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  1. Ofer Feinerman
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  2. Bernhard Haeupler
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Correspondence to Amos Korman.

Additional information

O.F. was supported in part by the Clore Foundation, the Israel Science Foundation (FIRST Grant No. 1694/10) and the Minerva Foundation. B.H. was supported in part by the NSF Grant Distributed Algorithms for Near-Planar Networks. A.K. was supported in part by the ANR project DISPLEXITY, and by the INRIA project GANG. This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 648032).

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Feinerman, O., Haeupler, B. & Korman, A. Breathe before speaking: efficient information dissemination despite noisy, limited and anonymous communication. Distrib. Comput. 30, 339–355 (2017). https://doi.org/10.1007/s00446-015-0249-4

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