58,845 research outputs found

    Plurality consensus in arbitrary graphs : lessons learned from load balancing.

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    We consider plurality consensus in networks of n nodes. Initially, each node has one of k opinions. The nodes execute a (randomized) distributed protocol to agree on the plurality opinion (the opinion initially supported by the most nodes). In certain types of networks the nodes can be quite cheap and simple, and hence one seeks protocols that are not only time efficient but also simple and space efficient. Typically, protocols depend heavily on the employed communication mechanism, which ranges from sequential (only one pair of nodes communicates at any time) to fully parallel (all nodes communicate with all their neighbors at once) and everything in-between. We propose a framework to design protocols for a multitude of communication mechanisms. We introduce protocols that solve the plurality consensus problem and are, with probability 1-o(1), both time and space efficient. Our protocols are based on an interesting relationship between plurality consensus and distributed load balancing. This relationship allows us to design protocols that generalize the state of the art for a large range of problem parameters

    Plurality Consensus in Arbitrary Graphs: Lessons Learned from Load Balancing

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    We consider plurality consensus in networks of n nodes. Initially, each node has one of k opinions. The nodes execute a (randomized) distributed protocol to agree on the plurality opinion (the opinion initially supported by the most nodes). In certain types of networks the nodes can be quite cheap and simple, and hence one seeks protocols that are not only time efficient but also simple and space efficient. Typically, protocols depend heavily on the employed communication mechanism, which ranges from sequential (only one pair of nodes communicates at any time) to fully parallel (all nodes communicate with all their neighbors at once) and everything in-between. We propose a framework to design protocols for a multitude of communication mechanisms. We introduce protocols that solve the plurality consensus problem and are, with probability 1-o(1), both time and space efficient. Our protocols are based on an interesting relationship between plurality consensus and distributed load balancing. This relationship allows us to design protocols that generalize the state of the art for a large range of problem parameters

    Fast Deterministic Consensus in a Noisy Environment

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    It is well known that the consensus problem cannot be solved deterministically in an asynchronous environment, but that randomized solutions are possible. We propose a new model, called noisy scheduling, in which an adversarial schedule is perturbed randomly, and show that in this model randomness in the environment can substitute for randomness in the algorithm. In particular, we show that a simplified, deterministic version of Chandra's wait-free shared-memory consensus algorithm (PODC, 1996, pp. 166-175) solves consensus in time at most logarithmic in the number of active processes. The proof of termination is based on showing that a race between independent delayed renewal processes produces a winner quickly. In addition, we show that the protocol finishes in constant time using quantum and priority-based scheduling on a uniprocessor, suggesting that it is robust against the choice of model over a wide range.Comment: Typographical errors fixe

    Randomized protocols for asynchronous consensus

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    The famous Fischer, Lynch, and Paterson impossibility proof shows that it is impossible to solve the consensus problem in a natural model of an asynchronous distributed system if even a single process can fail. Since its publication, two decades of work on fault-tolerant asynchronous consensus algorithms have evaded this impossibility result by using extended models that provide (a) randomization, (b) additional timing assumptions, (c) failure detectors, or (d) stronger synchronization mechanisms than are available in the basic model. Concentrating on the first of these approaches, we illustrate the history and structure of randomized asynchronous consensus protocols by giving detailed descriptions of several such protocols.Comment: 29 pages; survey paper written for PODC 20th anniversary issue of Distributed Computin

    A Coordinate Descent Primal-Dual Algorithm and Application to Distributed Asynchronous Optimization

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    Based on the idea of randomized coordinate descent of α\alpha-averaged operators, a randomized primal-dual optimization algorithm is introduced, where a random subset of coordinates is updated at each iteration. The algorithm builds upon a variant of a recent (deterministic) algorithm proposed by V\~u and Condat that includes the well known ADMM as a particular case. The obtained algorithm is used to solve asynchronously a distributed optimization problem. A network of agents, each having a separate cost function containing a differentiable term, seek to find a consensus on the minimum of the aggregate objective. The method yields an algorithm where at each iteration, a random subset of agents wake up, update their local estimates, exchange some data with their neighbors, and go idle. Numerical results demonstrate the attractive performance of the method. The general approach can be naturally adapted to other situations where coordinate descent convex optimization algorithms are used with a random choice of the coordinates.Comment: 10 page

    Gossip Algorithms for Distributed Signal Processing

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    Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This article presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmitted messages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.Comment: Submitted to Proceedings of the IEEE, 29 page
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