between computers, and a resulting paradigm shift from centralized to highly distributed systems. With massive scale also comes massive instability, as node and link failures become the norm rather than the exception. For such highly volatile systems, decentralized gossip-based protocols are emerging as an approach to maintaining simplicity and scalability while achieving fault-tolerant information dissemination.

The dynamic behavior of a network in which information is changing continuously over time requires robust and efficient mechanisms for keeping nodes updated about new information. Gossip protocols are mechanisms for this task in which nodes communicate with one another according to some underlying deterministic or randomized algorithm, exchanging information in each communication step. In a variety of contexts, the use of randomization to propagate information has been found to provide better reliability and scalability than more regimented deterministic approaches. In many settings, such as a cluster of distributed computing hosts, new information is generated at individual nodes, and is most “interesting ” to nodes that are nearby. Thus, we propose distance-based propagation bounds as a performance measure for gossip mechanisms: a node at distance d from the origin of a new piece of information should be able to learn about this information with a delay that grows slowly with d, and is independent of the size of the network. For nodes arranged with uniform density in Euclidean space, we present natural gossip mechanisms, called spatial gossip, that satisfy such a guarantee: new information is spread to

Motivated by applications to sensor, peer-to-peer, and ad hoc networks, we study distributed algorithms, also known as gossip algorithms, for exchanging information and for computing in an arbitrarily connected network of nodes. The topology of such networks changes continuously as new nodes join and old nodes leave the network. Algorithms for such networks need to be robust against changes in topology. Additionally, nodes in sensor networks operate under limited computational, communication, and energy resources. These constraints have motivated the design of “gossip ” algorithms: schemes which distribute the computational burden and in which a node communicates with a randomly chosen neighbor. We analyze the averaging problem under the gossip constraint for an arbitrary network graph, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Designing the fastest gossip algorithm corresponds to minimizing this eigenvalue, which is a semidefinite program (SDP). In general, SDPs cannot be solved in a distributed fashion; however, exploiting problem structure, we propose a distributed subgradient method that solves the optimization problem over the network. The relation of averaging time to the second largest eigenvalue naturally relates it to the mixing time of a random walk with transition probabilities derived from the gossip algorithm. We use this connection to study the performance and scaling of gossip algorithms on two popular networks: Wireless Sensor Networks, which are modeled as Geometric Random Graphs, and the Internet graph under the so-called Preferential Connectivity (PC) model.

We study the problem of simultaneously disseminating multiple messages in a large network in a decentralized and distributed manner. We consider a network with n nodes and k (k = O(n)) messages spread throughout the network to start with, but not all nodes have all the messages. Our communication model is such that the nodes communicate in discrete-time steps, and in every time-step, each node communicates with a random communication partner chosen uniformly from all the nodes (known as the random phone call model). The system is bandwidth limited and in each time-step, only one message can be transmitted. The goal is to disseminate rapidly all the messages among all the nodes. We study the time required for this dissemination to occur with high probability, and also in expectation. We present a protocol based on random linear coding (RLC) that disseminates all the messages among all the nodes in O(n) time, which is order optimal, if we ignore the small overhead associated with each transmission. The overhead does not depend on the size of the messages and is less than 1 % for k = 100 and messages of size 100 KB. We also consider a store and forward mechanism without coding, which is a natural extension of gossip-based dissemination with one message in the network. We show that, such an uncoded scheme can do no better than a sequential approach (instead of doing it simultaneously) of disseminating the messages which takes Θ(n ln(n)) time, since disseminating a single message in a gossip network takes Θ(ln(n)) time. 1

Abstract—The problem of computing functions of values at the nodes in a network in a fully distributed manner, where nodes do not have unique identities and make decisions based only on local information, has applications in sensor, peer-to-peer, and adhoc networks. The task of computing separable functions, which can be written as linear combinations of functions of individual variables, is studied in this context. Known iterative algorithms for averaging can be used to compute the normalized values of such functions, but these algorithms do not extend in general to the computation of the actual values of separable functions. The main contribution of this paper is the design of a distributed randomized algorithm for computing separable functions. The running time of the algorithm is shown to depend on the running time of a minimum computation algorithm used as a subroutine. Using a randomized gossip mechanism for minimum computation as the subroutine yields a complete fully distributed algorithm for computing separable functions. For a class of graphs with small spectral gap, such as grid graphs, the time used by the algorithm to compute averages is of a smaller order than the time required by a known iterative averaging scheme. Index Terms—Data aggregation, distributed algorithms, gossip algorithms, randomized algorithms. I.

In this paper we investigate distributed computation in dynamic networks in which the network topology changes from round to round. We consider a worst-case model in which the communication links for each round are chosen by an adversary, and nodes do not know who their neighbors for the current round are before they broadcast their messages. The model allows the study of the fundamental computation power of dynamic networks. In particular, it captures mobile networks and wireless networks, in which mobility and interference render communication unpredictable. In contrast to much of the existing work on dynamic networks, we do not assume that the network eventually stops changing; we require correctness and termination even in networks that change continually. We introduce a stability property called

Motivated by applications to sensor and ad hoc networks, we study distributed algorithms for passing information and for computing averages in an arbitrarily connected network of nodes. Our work draws upon and contributes to a growing body of literature in three areas: (i) Distributed averaging algorithms, as formulated in Kempe, Dobra and Gehrke (2003), (ii) geometric random graph models for large networks of sensors, as put forth in Gupta and Kumar (2000), and (iii) the fastest mixing Markov chain on a graph, as studied recently in Boyd, Diaconis and Xiao (2003). For distributed averaging...

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.

We study deterministic gossiping in synchronous systems with dynamic crash failures. Each processor is initialized with an input value called rumor. In the standard gossip problem, the goal of every processor is to learn all the rumors. When processors may crash, then this goal needs to be revised, since it is possible, at a point in an execution, that certain rumors are known only to processors that have already crashed. We define gossiping to be completed, for a system with crashes, when every processor knows either the rumor of processor v or that v has already crashed, for any processor v. We design gossiping algorithms that are efficient with respect to both time and communication. Let t < n be the number of failures, where n is the number of processors. If n − t = Ω(n/polylog n), then one of our algorithms completes gossiping in O(log 2 t) time and with O(n polylog n) messages. We develop an algorithm that performs gossiping with O(n 1.77) messages and in O(log 2 n) time, in any execution in which at least one processor remains non-faulty. We show a trade-off between time and communication in gossiping algorithms: if the number of messages is at most O(n polylog n), then the time has to be at least Ω ( log n. By way of application, we show that if n − t = Ω(n), then log(n log n)−log t consensus can be solved in O(t) time and with O(n log 2 t) messages.

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