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

A Decentralized Lifetime Maximization Algorithm for Distributed Applications in Wireless Sensor Networks

We consider the scenario of a Wireless Sensor Networks (WSN) where the nodes are equipped with a programmable middleware that allows for quickly deploying different applications running on top of it so as to follow the changing ambient needs. We then address the problem of finding the optimal deployment of the target applications in terms of network lifetime. We approach the problem considering every possible decomposition of an application's sensing and computing operations into tasks to be assigned to each infrastructure component. The contribution of energy consumption due to the energy cost of each task is then considered into local cost functions in each node, allowing us to evaluate the viability of the deployment solution. The proposed algorithm is based on an iterative and asynchronous local optimization of the task allocations between neighboring nodes that increases the network lifetime. Simulation results show that our framework leads to considerable energy saving with respect to both sink-oriented and cluster-oriented deployment approaches, particularly for networks with high node densities and non-uniform energy consumption or initial battery charge

The extended epoch of galaxy formation: age dating of ~3600 galaxies with 2<z<6.5 in the VIMOS Ultra-Deep Survey

We aim at improving constraints on the epoch of galaxy formation by measuring the ages of 3597 galaxies with spectroscopic redshifts 2<z<6.5 in the VIMOS Ultra Deep Survey (VUDS). We derive ages and other physical parameters from the simultaneous fitting with the GOSSIP+ software of observed UV rest-frame spectra and photometric data from the u-band up to 4.5 microns using composite stellar population models. We conclude from extensive simulations that at z>2 the joint analysis of spectroscopy and photometry combined with restricted age possibilities when taking into account the age of the Universe substantially reduces systematic uncertainties and degeneracies in the age derivation. We find galaxy ages ranging from very young with a few tens of million years to substantially evolved with ages up to ~1.5-2 Gyr. The formation redshifts z_f derived from the measured ages indicate that galaxies may have started forming stars as early as z_f~15. We produce the formation redshift function (FzF), the number of galaxies per unit volume formed at a redshift z_f, and compare the FzF in increasing redshift bins finding a remarkably constant 'universal' FzF. The FzF is parametrized with (1+z)^\zeta, with \zeta~0.58+/-0.06, indicating a smooth 2 dex increase from z~15 to z~2. Remarkably this observed increase is of the same order as the observed rise in the star formation rate density (SFRD). The ratio of the SFRD with the FzF gives an average SFR per galaxy of ~7-17Msun/yr at z~4-6, in agreement with the measured SFR for galaxies at these redshifts. From the smooth rise in the FzF we infer that the period of galaxy formation extends from the highest possible redshifts that we can probe at z~15 down to redshifts z~2. This indicates that galaxy formation is a continuous process over cosmic time, with a higher number of galaxies forming at the peak in SFRD at z~2 than at earlier epochs. (Abridged)Comment: Submitted to A&A, 24 page

GCP: Gossip-based Code Propagation for Large-scale Mobile Wireless Sensor Networks

Wireless sensor networks (WSN) have recently received an increasing interest. They are now expected to be deployed for long periods of time, thus requiring software updates. Updating the software code automatically on a huge number of sensors is a tremendous task, as ''by hand'' updates can obviously not be considered, especially when all participating sensors are embedded on mobile entities. In this paper, we investigate an approach to automatically update software in mobile sensor-based application when no localization mechanism is available. We leverage the peer-to-peer cooperation paradigm to achieve a good trade-off between reliability and scalability of code propagation. More specifically, we present the design and evaluation of GCP ({\emph Gossip-based Code Propagation}), a distributed software update algorithm for mobile wireless sensor networks. GCP relies on two different mechanisms (piggy-backing and forwarding control) to improve significantly the load balance without sacrificing on the propagation speed. We compare GCP against traditional dissemination approaches. Simulation results based on both synthetic and realistic workloads show that GCP achieves a good convergence speed while balancing the load evenly between sensors

Greedy Gossip with Eavesdropping

This paper presents greedy gossip with eavesdropping (GGE), a novel randomized gossip algorithm for distributed computation of the average consensus problem. In gossip algorithms, nodes in the network randomly communicate with their neighbors and exchange information iteratively. The algorithms are simple and decentralized, making them attractive for wireless network applications. In general, gossip algorithms are robust to unreliable wireless conditions and time varying network topologies. In this paper we introduce GGE and demonstrate that greedy updates lead to rapid convergence. We do not require nodes to have any location information. Instead, greedy updates are made possible by exploiting the broadcast nature of wireless communications. During the operation of GGE, when a node decides to gossip, instead of choosing one of its neighbors at random, it makes a greedy selection, choosing the node which has the value most different from its own. In order to make this selection, nodes need to know their neighbors' values. Therefore, we assume that all transmissions are wireless broadcasts and nodes keep track of their neighbors' values by eavesdropping on their communications. We show that the convergence of GGE is guaranteed for connected network topologies. We also study the rates of convergence and illustrate, through theoretical bounds and numerical simulations, that GGE consistently outperforms randomized gossip and performs comparably to geographic gossip on moderate-sized random geometric graph topologies.Comment: 25 pages, 7 figure

Reliable and timely event notification for publish/subscribe services over the internet

The publish/subscribe paradigm is gaining attention for the development of several applications in wide area networks (WANs) due to its intrinsic time, space, and synchronization decoupling properties that meet the scalability and asynchrony requirements of those applications. However, while the communication in a WAN may be affected by the unpredictable behavior of the network, with messages that can be dropped or delayed, existing publish/subscribe solutions pay just a little attention to addressing these issues. On the contrary, applications such as business intelligence, critical infrastructures, and financial services require delivery guarantees with strict temporal deadlines. In this paper, we propose a framework that enforces both reliability and timeliness for publish/subscribe services over WAN. Specifically, we combine two different approaches: gossiping, to retrieve missing packets in case of incomplete information, and network coding, to reduce the number of retransmissions and, consequently, the latency. We provide an analytical model that describes the information recovery capabilities of our algorithm and a simulation-based study, taking into account a real workload from the Air Traffic Control domain, which evidences how the proposed solution is able to ensure reliable event notification over a WAN within a reasonable bounded time window. © 2013 IEEE

Cooperative Convex Optimization in Networked Systems: Augmented Lagrangian Algorithms with Directed Gossip Communication

We study distributed optimization in networked systems, where nodes cooperate to find the optimal quantity of common interest, x=x^\star. The objective function of the corresponding optimization problem is the sum of private (known only by a node,) convex, nodes' objectives and each node imposes a private convex constraint on the allowed values of x. We solve this problem for generic connected network topologies with asymmetric random link failures with a novel distributed, decentralized algorithm. We refer to this algorithm as AL-G (augmented Lagrangian gossiping,) and to its variants as AL-MG (augmented Lagrangian multi neighbor gossiping) and AL-BG (augmented Lagrangian broadcast gossiping.) The AL-G algorithm is based on the augmented Lagrangian dual function. Dual variables are updated by the standard method of multipliers, at a slow time scale. To update the primal variables, we propose a novel, Gauss-Seidel type, randomized algorithm, at a fast time scale. AL-G uses unidirectional gossip communication, only between immediate neighbors in the network and is resilient to random link failures. For networks with reliable communication (i.e., no failures,) the simplified, AL-BG (augmented Lagrangian broadcast gossiping) algorithm reduces communication, computation and data storage cost. We prove convergence for all proposed algorithms and demonstrate by simulations the effectiveness on two applications: l_1-regularized logistic regression for classification and cooperative spectrum sensing for cognitive radio networks.Comment: 28 pages, journal; revise