Consensus Needs Broadcast in Noiseless Models but can be Exponentially Easier in the Presence of Noise

Consensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast, and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent. We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An $\Omega(\epsilon^{-2} n)$ lower bound on the number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS Comp. Bio. 2018] in one such model (noisy uniform PULL, where $\epsilon$ is a parameter that measures the amount of noise). In such model, we prove a new $\Theta(\epsilon^{-2} n \log n)$ bound for Broadcast and a $\Theta(\epsilon^{-2} \log n)$ bound for binary Consensus, thus establishing an exponential gap between the number of rounds necessary for Consensus versus Broadcast

Consensus vs Broadcast, with and without Noise

International audienceConsensus and Broadcast are two fundamental problems in distributed computing, whose solutions have several applications. Intuitively, Consensus should be no harder than Broadcast , and this can be rigorously established in several models. Can Consensus be easier than Broadcast? In models that allow noiseless communication, we prove a reduction of (a suitable variant of) Broadcast to binary Consensus, that preserves the communication model and all complexity parameters such as randomness, number of rounds, communication per round, etc., while there is a loss in the success probability of the protocol. Using this reduction, we get, among other applications, the first logarithmic lower bound on the number of rounds needed to achieve Consensus in the uniform GOSSIP model on the complete graph. The lower bound is tight and, in this model, Consensus and Broadcast are equivalent. We then turn to distributed models with noisy communication channels that have been studied in the context of some bio-inspired systems. In such models, only one noisy bit is exchanged when a communication channel is established between two nodes, and so one cannot easily simulate a noiseless protocol by using error-correcting codes. An Ω(ε −2 n) lower bound on the number of rounds needed for Broadcast is proved by Boczkowski et al. [PLOS Comp. Bio. 2018] in one such model (noisy uniform PULL, where ε is a parameter that measures the amount of noise). We prove an O(ε −2 log n) upper bound for binary Consensus in such model, thus establishing an exponential gap between the number of rounds necessary for Consensus versus Broadcast. We also prove a new O(ε −2 n log n) upper bound for Broadcast in this model

Distributed Parameter Estimation via Pseudo-likelihood

Estimating statistical models within sensor networks requires distributed algorithms, in which both data and computation are distributed across the nodes of the network. We propose a general approach for distributed learning based on combining local estimators defined by pseudo-likelihood components, encompassing a number of combination methods, and provide both theoretical and experimental analysis. We show that simple linear combination or max-voting methods, when combined with second-order information, are statistically competitive with more advanced and costly joint optimization. Our algorithms have many attractive properties including low communication and computational cost and "any-time" behavior.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

SEGMENT3D: A Web-based Application for Collaborative Segmentation of 3D images used in the Shoot Apical Meristem

The quantitative analysis of 3D confocal microscopy images of the shoot apical meristem helps understanding the growth process of some plants. Cell segmentation in these images is crucial for computational plant analysis and many automated methods have been proposed. However, variations in signal intensity across the image mitigate the effectiveness of those approaches with no easy way for user correction. We propose a web-based collaborative 3D image segmentation application, SEGMENT3D, to leverage automatic segmentation results. The image is divided into 3D tiles that can be either segmented interactively from scratch or corrected from a pre-existing segmentation. Individual segmentation results per tile are then automatically merged via consensus analysis and then stitched to complete the segmentation for the entire image stack. SEGMENT3D is a comprehensive application that can be applied to other 3D imaging modalities and general objects. It also provides an easy way to create supervised data to advance segmentation using machine learning models

The asymptotical error of broadcast gossip averaging algorithms

In problems of estimation and control which involve a network, efficient distributed computation of averages is a key issue. This paper presents theoretical and simulation results about the accumulation of errors during the computation of averages by means of iterative "broadcast gossip" algorithms. Using martingale theory, we prove that the expectation of the accumulated error can be bounded from above by a quantity which only depends on the mixing parameter of the algorithm and on few properties of the network: its size, its maximum degree and its spectral gap. Both analytical results and computer simulations show that in several network topologies of applicative interest the accumulated error goes to zero as the size of the network grows large.Comment: 10 pages, 3 figures. Based on a draft submitted to IFACWC201

Dynamical and topological aspects of consensus formation in complex networks

The present work analyzes a particular scenario of consensus formation, where the individuals navigate across an underlying network defining the topology of the walks. The consensus, associated to a given opinion coded as a simple message, is generated by interactions during the agent's walk and manifest itself in the collapse of the various opinions into a single one. We analyze how the topology of the underlying networks and the rules of interaction between the agents promote or inhibit the emergence of this consensus. We find that non-linear interaction rules are required to form consensus and that consensus is more easily achieved in networks whose degree distribution is narrower.Fil: Chacoma, Andrés Alberto. Comisión Nacional de Energía Atómica. Gerencia del Area de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; ArgentinaFil: Mato, German. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Kuperman, Marcelo Nestor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentin