Gossip Algorithms for Distributed Signal Processing

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

On the Role of Mobility for Multi-message Gossip

We consider information dissemination in a large $n$-user wireless network in which $k$ users wish to share a unique message with all other users. Each of the $n$ users only has knowledge of its own contents and state information; this corresponds to a one-sided push-only scenario. The goal is to disseminate all messages efficiently, hopefully achieving an order-optimal spreading rate over unicast wireless random networks. First, we show that a random-push strategy -- where a user sends its own or a received packet at random -- is order-wise suboptimal in a random geometric graph: specifically, $\Omega(\sqrt{n})$ times slower than optimal spreading. It is known that this gap can be closed if each user has "full" mobility, since this effectively creates a complete graph. We instead consider velocity-constrained mobility where at each time slot the user moves locally using a discrete random walk with velocity $v(n)$ that is much lower than full mobility. We propose a simple two-stage dissemination strategy that alternates between individual message flooding ("self promotion") and random gossiping. We prove that this scheme achieves a close to optimal spreading rate (within only a logarithmic gap) as long as the velocity is at least $v(n)=\omega(\sqrt{\log n/k})$. The key insight is that the mixing property introduced by the partial mobility helps users to spread in space within a relatively short period compared to the optimal spreading time, which macroscopically mimics message dissemination over a complete graph.Comment: accepted to IEEE Transactions on Information Theory, 201

Gossip vs. Markov Chains, and Randomness-Efficient Rumor Spreading

We study gossip algorithms for the rumor spreading problem which asks one node to deliver a rumor to all nodes in an unknown network. We present the first protocol for any expander graph $G$ with $n$ nodes such that, the protocol informs every node in $O(\log n)$ rounds with high probability, and uses $\tilde{O}(\log n)$ random bits in total. The runtime of our protocol is tight, and the randomness requirement of $\tilde{O}(\log n)$ random bits almost matches the lower bound of $\Omega(\log n)$ random bits for dense graphs. We further show that, for many graph families, polylogarithmic number of random bits in total suffice to spread the rumor in $O(\mathrm{poly}\log n)$ rounds. These results together give us an almost complete understanding of the randomness requirement of this fundamental gossip process. Our analysis relies on unexpectedly tight connections among gossip processes, Markov chains, and branching programs. First, we establish a connection between rumor spreading processes and Markov chains, which is used to approximate the rumor spreading time by the mixing time of Markov chains. Second, we show a reduction from rumor spreading processes to branching programs, and this reduction provides a general framework to derandomize gossip processes. In addition to designing rumor spreading protocols, these novel techniques may have applications in studying parallel and multiple random walks, and randomness complexity of distributed algorithms.Comment: 41 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1304.135

Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them

Distributed Detection and Estimation in Wireless Sensor Networks

In this article we consider the problems of distributed detection and estimation in wireless sensor networks. In the first part, we provide a general framework aimed to show how an efficient design of a sensor network requires a joint organization of in-network processing and communication. Then, we recall the basic features of consensus algorithm, which is a basic tool to reach globally optimal decisions through a distributed approach. The main part of the paper starts addressing the distributed estimation problem. We show first an entirely decentralized approach, where observations and estimations are performed without the intervention of a fusion center. Then, we consider the case where the estimation is performed at a fusion center, showing how to allocate quantization bits and transmit powers in the links between the nodes and the fusion center, in order to accommodate the requirement on the maximum estimation variance, under a constraint on the global transmit power. We extend the approach to the detection problem. Also in this case, we consider the distributed approach, where every node can achieve a globally optimal decision, and the case where the decision is taken at a central node. In the latter case, we show how to allocate coding bits and transmit power in order to maximize the detection probability, under constraints on the false alarm rate and the global transmit power. Then, we generalize consensus algorithms illustrating a distributed procedure that converges to the projection of the observation vector onto a signal subspace. We then address the issue of energy consumption in sensor networks, thus showing how to optimize the network topology in order to minimize the energy necessary to achieve a global consensus. Finally, we address the problem of matching the topology of the network to the graph describing the statistical dependencies among the observed variables.Comment: 92 pages, 24 figures. To appear in E-Reference Signal Processing, R. Chellapa and S. Theodoridis, Eds., Elsevier, 201

Privacy Preserving Randomized Gossip Algorithms

In this work we present three different randomized gossip algorithms for solving the average consensus problem while at the same time protecting the information about the initial private values stored at the nodes. We give iteration complexity bounds for all methods, and perform extensive numerical experiments.Comment: 38 page

Distributed Big-Data Optimization via Block-Iterative Convexification and Averaging

In this paper, we study distributed big-data nonconvex optimization in multi-agent networks. We consider the (constrained) minimization of the sum of a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a convex (possibly) nonsmooth regularizer. Our interest is in big-data problems wherein there is a large number of variables to optimize. If treated by means of standard distributed optimization algorithms, these large-scale problems may be intractable, due to the prohibitive local computation and communication burden at each node. We propose a novel distributed solution method whereby at each iteration agents optimize and then communicate (in an uncoordinated fashion) only a subset of their decision variables. To deal with non-convexity of the cost function, the novel scheme hinges on Successive Convex Approximation (SCA) techniques coupled with i) a tracking mechanism instrumental to locally estimate gradient averages; and ii) a novel block-wise consensus-based protocol to perform local block-averaging operations and gradient tacking. Asymptotic convergence to stationary solutions of the nonconvex problem is established. Finally, numerical results show the effectiveness of the proposed algorithm and highlight how the block dimension impacts on the communication overhead and practical convergence speed