Abstract not found

Average consensus consists in the problem of determining the average of some quantities by means of a distributed algorithm. It is a simple instance of problems arising when designing estimation algorithms operating on data produced by sensor networks. Simple solutions based on linear estimation algorithms have already been proposed in the literature and their performance has been analyzed in detail. If the communication links which allow the data exchange between the sensors have some loss, then the estimation performance will degrade. In this contribution the performance degradation due to this data loss is evaluated.

We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set. The objective function is defined by a sum of local objective functions, while the global constraint set is produced by the intersection of local constraint sets. In particular, we study two cases: one where the equality constraint is absent, and the other where the local constraint sets are identical. We devise two distributed primal-dual subgradient algorithms based on the characterization of the primal-dual optimal solutions as the saddle points of the Lagrangian and penalty functions. These algorithms can be implemented over networks with dynamically changing topologies but satisfying a standard connectivity property, and allow the agents to asymptotically agree on optimal solutions and optimal values of the optimization problem under the Slater’s condition.

Gossip-based algorithms were first introduced for reliably disseminating data in large-scale distributed systems. However, their simplicity, robustness, and flexibility make them attractive for more than just pure data dissemination alone. In particular, gossiping has been applied to data aggregation, overlay maintenance, and resource allocation. Gossiping applications more or less fit the same framework, with often subtle differences in algorithmic details determining divergent emergent behavior. This divergence is often difficult to understand, as formal models have yet to be developed that can capture the full design space of gossiping solutions. In this paper, we present a brief introduction to the field of gossiping in distributed systems, by providing a simple framework and using that framework to describe solutions for various application domains.

Abstract not found

communication

In peer-to-peer (P2P) networks, reputation aggregation and peer ranking are the most time-consuming and spacedemanding operations. This paper proposes a gossip-based reputation system (GossipTrust) for fast aggregation of global reputation scores. It leverages a Bloom filter based scheme for efficient score ranking. GossipTrust does not require any secure hashing or fast lookup mechanism, thus is applicable to both unstructured and structured P2P networks. Randomized gossiping with effective use of power nodes enables fast aggregation and fast dissemination of global scores in O(log2 n) time steps, where n is the network size. The gossip-based protocol is designed to tolerate dynamic peer joining and departure, as well as to avoid possible peer collusions. The scheme has a considerably low gossiping message overhead, i.e. O(nlog2 n) messages for n nodes. Bloom filters reduce the memory overhead per node to 512 KB for a 10,000-node network. We evaluate the performance of GossipTrust with both P2P file-sharing and parameter-sweeping applications. The simulation results demonstrate that GossipTrust has small aggregation time, low memory demand, and high ranking accuracy. These results suggest promising advantages of using the GossipTrust system for trusted P2P computing.

In a sensor network, in practice, the communication among sensors is subject to: (1) errors or failures at random times; (2) costs; and (3) constraints since sensors and networks operate under scarce resources, such as power, data rate, or communication. The signal-to-noise ratio (SNR) is usually a main factor in determining the probability of error (or of communication failure) in a link. These probabilities are then a proxy for the SNR under which the links operate. The paper studies the problem of designing the topology, i.e., assigning the probabilities of reliable communication among sensors (or of link failures) to maximize the rate of convergence of average consensus, when the link communication costs are taken into account, and there is an overall communication budget constraint. To consider this problem, we address a number of preliminary issues: (1) model the network as a random topology; (2) establish necessary and sufficient conditions for mean square sense (mss) and almost sure (a.s.) convergence of average consensus when network links fail; and, in particular, (3) show that a necessary and sufficient condition for both mss and a.s. convergence is for the algebraic connectivity of the mean graph describing the network topology to be strictly positive. With these results, we formulate topology design, subject to random link failures and to a communication cost constraint, as a constrained convex optimization problem to which we apply semidefinite programming techniques. We show by an extensive numerical study that the optimal design improves significantly the convergence speed of the consensus algorithm and can achieve the asymptotic performance of a non-random network at a fraction of the communication cost.

We propose and analyse a quasirandom analogue to the classical push model for disseminating information in networks (“randomized rumor spreading”). In the classical model, in each round each informed node chooses a neighbor at random and informs it. Results of Frieze and Grimmett (Discrete Appl. Math. 1985) show that this simple protocol succeeds in spreading a rumor from one node of a complete graph to all others within O(log n) rounds. For the network being a hypercube or a random graph G(n, p) with p ≥ (1+ε)(log n)/n, also O(log n) rounds suffice (Feige, Peleg, Raghavan, and Upfal, Random Struct. Algorithms 1990). In the quasirandom model, we assume that each node has a (cyclic) list of its neighbors. Once informed, it starts at a random position of the list, but from then on informs its neighbors in the order of the list. Surprisingly, irrespective of the orders of the lists, the above mentioned bounds still hold. In addition, we also show a O(log n) bound for sparsely connected random graphs G(n, p) with p = (log n+f(n))/n, where f(n) → ∞ and f(n) = O(log log n). Here, the classical model needs Θ(log 2 (n)) rounds. Hence the quasirandom model achieves similar or better broadcasting times with a greatly reduced use of random bits.

This paper considers the average consensus problem on a network of digital links, and proposes a set of algorithms based on pairwise “gossip” communications and updates. We study the convergence properties of such algorithms with the goal of answering two design questions, arising from the literature: whether the agents should encode their communication by a deterministic or a randomized quantizer, and whether they should use, and how, exact information regarding their own states in the update.