Efficient and Noise-Resilient rumor-spreading in Large, Anonymous Populations.
Year: 2013
Type: preprint
Abstract: The study in this paper aims to further our understanding of communication in large anonymous populations composed of simple agents which interact through short and highly unreliable messages. We focus on the rumorspreading problem, one of the main fundamental tasks in distributed computing, and initiate the study of reliable rumor-spreading under communication noise. Specifically, the noisy rumor-spreading problem considers a population of n anonymous agents, with one distinguished source agent representing the environment associated with an opinion (a bit B ∈ {0, 1}). Few agents obtain noisy samples of this bit and all agents use noisy interactions to guarantee that eventually, all agents hold the correct opinion B with high probability. We also consider a natural variant of this problem, called the noisy majority-spreading problem, where initially the agents in some subset X of the population are informed with opinions in {0, 1}, such that the majority opinion B among the agents in X has some non-negligible bias over the other opinion. The goal of agents is to use their (noisy) interactions to obtain B with high probability. Our model for communication is extremely weak and follows the push gossip communication paradigm: In each synchronous round each agent that wishes to send information delivers a message to a randomly chosen anonymous agent. Since our objective is to study restricted communication channels, we assume that each message can contain only one bit (essentially representing an opinion). The system is furthermore assumed to be so noisy that the bit in each message sent is flipped independently with probability 1/2− ǫ, for small ǫ, that is, it carries only H(ǫ) amount of entropy. Even in this severely restricted, stochastic and noisy setting we give natural protocols that solve the noisy rumorspreading and the noisy majority-spreading problems efficiently. In particular, our protocols run in O( 1 ǫ 2 log n) rounds and use O( 1 ǫ 2n log n) messages (or bits) in total. These bounds are both asymptotically optimal and, in fact, are as fast and message efficient as if each agent would have been simultaneously informed by the environment directly. 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 natural populations.
Source: arXiv (Cornell University)
Authors: Ofer Feinerman, Bernhard Haeupler, Amos Korman
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1820044090