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, Ω(√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)=ω(√(logn 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.
Finally, we note that gossip algorithms have also been employed and analyzed for other scenarios like distributed averaging, where each node is willing to compute the average of all initial values given at all nodes in a decentralized manner, e.g. @cite_34 @cite_3 . The objective of such distributed consensus is to minimize the total number of computations. It turns out that the convergence rates of both message sharing and distributed averaging are largely dependent on the eigenvalues or, more specifically, the mixing times of the graph matrices associated with the network geometry @cite_3 @cite_16 .
@cite_34 @cite_3 @cite_16
1547358136 2117905067
Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and for computing in an arbitrarily connected network of nodes. Specifically, we propose a broadcasting-based gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithms almost surely converge to a consensus. In addition, the random consensus value is, in expectation, equal to the desired value, i.e., the average of initial node measurements. However, the broadcast gossip algorithms do not converge to the initial average in absolute sense because of the fact that the sum is not preserved at every iteration. We provide theoretical results on the mean square error performance of the broadcast gossip algorithms. The results indicate that the mean square error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithms required to achieve a given distance to consensus through numerical simulations. Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcasting-based gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithm converges almost surely to a consensus. We prove that the random consensus value is, in expectation, the average of initial node measurements and that it can be made arbitrarily close to this value in mean squared error sense, under a balanced connectivity model and by trading off convergence speed with accuracy of the computation. We provide theoretical and numerical results on the mean square error performance, on the convergence rate and study the effect of the ldquomixing parameterrdquo on the convergence rate of the broadcast gossip algorithm. The results indicate that the mean squared error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithm to achieve a given distance to consensus through theoretical and numerical results. Distributed averaging describes a class of network algorithms for the decentralized computation of aggregate statistics. Initially, each node has a scalar data value, and the goal is to compute the average of these values at every node (the so-called average consensus problem). Nodes iteratively exchange information with their neighbors and perform local updates until the value at every node converges to the initial network average. Much previous work has focused on algorithms where each node maintains and updates a single value; every time an update is performed, the previous value is forgotten. Convergence to the average consensus is achieved asymptotically. The convergence rate is fundamentally limited by network connectivity, and it can be prohibitively slow on topologies such as grids and random geometric graphs, even if the update rules are optimized. In this paper, we provide the first theoretical demonstration that adding a local prediction component to the update rule can significantly improve the convergence rate of distributed averaging algorithms. We focus on the case where the local predictor is a linear combination of the node's current and previous values (i.e., two memory taps), and our update rule computes a combination of the predictor and the usual weighted linear combination of values received from neighboring nodes. We derive the optimal mixing parameter for combining the predictor with the neighbors' values, and conduct a theoretical analysis of the improvement in convergence rate that can be achieved using this acceleration methodology. For a chain topology on N nodes, this leads to a factor of N improvement over standard consensus, and for a two-dimensional grid, our approach achieves a factor of ?N improvement. 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. Motivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, we have recently proposed a broadcasting-based gossiping protocol to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. The class of broadcast gossip algorithms achieve consensus almost surely at a value that is in the neighborhood of the initial node measurements? average. In this paper, we further study the broadcast gossip algorithms: we derive and analyze the optimal mixing parameter of the algorithm when approached from worst-case convergence rate, present theoretical results on limiting mean square error performance of the algorithm, and find the convergence rate order of the proposed protocol. Motivated by applications to sensor, peer-to-peer and ad hoc networks, we study distributed asynchronous algorithms, also known as gossip algorithms, for computation and information exchange in an arbitrarily connected network of nodes. Nodes in such networks operate under limited computational, communication and energy resources. These constraints naturally give rise to "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 arbitrary network, and find that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Using recent results of Boyd, Diaconis and Xiao (2003), we show that minimizing this quantity to design the fastest averaging algorithm on the network is a semi-definite program (SDP). In general, SDPs cannot be solved distributedly; however, exploiting problem structure, we propose a subgradient method that distributedly 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 that are derived from the gossip algorithm. We use this connection to study the performance of gossip algorithm on two popular networks: wireless sensor networks, which are modeled as geometric random graphs, and the Internet graph under the so-called preferential connectivity model. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . We study the distributed averaging problem on an arbitrary network with a gossip constraint, which means that no node communicates with more than one neighbour in every time slot. We consider algorithms which are linear iterations, where each iteration is described by a random matrix picked i.i.d. from some distribution. We derive conditions that this distribution must satisfy so that the sequence of iterations converges to the vector of averages in different senses. We then analyze a simple asynchronous randomized gossip algorithm for averaging, and show that the problem of optimizing the parameters of this algorithm for fastest convergence is a semi-definite program. Finally we study the relation between Markov chains and the averaging problem, and relate the averaging time of the algorithm to the mixing time of a related Markov chain on the graph. In this paper, we develop algorithms for distributed computation of averages of the node data over networks with bandwidth power constraints or large volumes of data. Distributed averaging algorithms fail to achieve consensus when deterministic uniform quantization is adopted. We propose a distributed algorithm in which the nodes utilize probabilistically quantized information, i.e., dithered quantization, to communicate with each other. The algorithm we develop is a dynamical system that generates sequences achieving a consensus at one of the quantization values almost surely. In addition, we show that the expected value of the consensus is equal to the average of the original sensor data. We derive an upper bound on the mean-square-error performance of the probabilistically quantized distributed averaging (PQDA). Moreover, we show that the convergence of the PQDA is monotonic by studying the evolution of the minimum-length interval containing the node values. We reveal that the length of this interval is a monotonically nonincreasing function with limit zero. We also demonstrate that all the node values, in the worst case, converge to the final two quantization bins at the same rate as standard unquantized consensus. Finally, we report the results of simulations conducted to evaluate the behavior and the effectiveness of the proposed algorithm in various scenarios. Average consensus and gossip algorithms have recently received significant attention, mainly because they constitute simple and robust algorithms for distributed information processing over networks. Inspired by heat diffusion, they compute the average of sensor networks measurements by iterating local averages until a desired level of convergence. Confronted with the diversity of these algorithms, the engineer may be puzzled in his choice for one of them. As an answer to his her need, we develop precise mathematical metrics, easy to use in practice, to characterize the convergence speed and the cost (time, message passing, energy...) of each of the algorithms. In contrast to other works focusing on time-invariant scenarios, we evaluate these metrics for ergodic time-varying networks. Our study is based on Oseledec's theorem, which gives an almost- sure description of the convergence speed of the algorithms of interest. We further provide upper bounds on the convergence speed. Finally, we use these tools to make some experimental observations illustrating the behavior of the convergence speed with respect to network topology and reliability in both average consensus and gossip algorithms. Motivated by applications to sensor, peer-to-peer, and ad-hoc networks, we study the problem of computing functions of values at the nodes in a network in a totally distributed manner. In particular, we consider separable functions, which can be written as linear combinations of functions of individual variables. 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 based on properties of exponential random variables. We bound the running time of our algorithm in terms of the running time of an information spreading algorithm used as a subroutine by the algorithm. Since we are interested in totally distributed algorithms, we consider a randomized gossip mechanism for information spreading as the subroutine. Combining these algorithms yields a complete and simple distributed algorithm for computing separable functions.The second contribution of this paper is an analysis of the information spreading time of the gossip algorithm. This analysis yields an upper bound on the information spreading time, and therefore a corresponding upper bound on the running time of the algorithm for computing separable functions, in terms of the conductance of an appropriate stochastic matrix. These bounds imply that, for a class of graphs with small spectral gap (such as grid graphs), the time used by our algorithm to compute averages is of a smaller order than the time required for the computation of averages by a known iterative gossip scheme [5]. In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature address the consensus averaging problem by distributed linear iterative algorithms, with asymptotic convergence of the consensus solution. The convergence rate of such distributed algorithms typically depends on the network topology and the weights given to the edges between neighboring sensors, as described by the network matrix. In this paper, we propose to accelerate the convergence rate for given network matrices by the use of polynomial filtering algorithms. The main idea of the proposed methodology is to apply a polynomial filter on the network matrix that will shape its spectrum in order to increase the convergence rate. Such an algorithm is equivalent to periodic updates in each of the sensors by aggregating a few of its previous estimates. We formulate the computation of the coefficients of the optimal polynomial as a semidefinite program that can be efficiently and globally solved for both static and dynamic network topologies. We finally provide simulation results that demonstrate the effectiveness of the proposed solutions in accelerating the convergence of distributed consensus averaging problems. 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 ad hoc 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. We present a study of anonymized data capturing a month of high-level communication activities within the whole of the Microsoft Messenger instant-messaging system. We examine characteristics and patterns that emerge from the collective dynamics of large numbers of people, rather than the actions and characteristics of individuals. The dataset contains summary properties of 30 billion conversations among 240 million people. From the data, we construct a communication graph with 180 million nodes and 1.3 billion undirected edges, creating the largest social network constructed and analyzed to date. We report on multiple aspects of the dataset and synthesized graph. We find that the graph is well-connected and robust to node removal. We investigate on a planetary-scale the oft-cited report that people are separated by "six degrees of separation" and find that the average path length among Messenger users is 6.6. We find that people tend to communicate more with each other when they have similar age, language, and location, and that cross-gender conversations are both more frequent and of longer duration than conversations with the same gender. Given a network of processes where each node has an initial scalar value, we consider the problem of computing their average asymptotically using a distributed, linear iterative algorithm. At each iteration, each node replaces its own value with a weighted average of its previous value and the values of its neighbors. We introduce the Metropolis weights, a simple choice for the averaging weights used in each step. We show that with these weights, the values at every node converge to the average, provided the innitely occurring communication graphs are jointly connected. Reaching consensus in a network is an important problem in control, estimation, and resource allocation. While many algorithms focus on computing the exact average of the initial values in the network, in some cases it is more important for nodes to reach a consensus quickly. In a distributed system establishing two-way communication may also be difficult or unreliable. In this paper, the effect of the wireless medium on simple consensus protocol is explored. In a wireless environment, a node's transmission is a broadcast to all nodes which can hear it, and due to signal propagation effects, the neighborhood size may change with time. A class of non-sum preserving algorithms involving unidirectional broadcasting is extended to a time-varying connection model. This algorithm converges almost surely and its expected consensus value is the true average. A simple bound is given on the convergence time. In decentralized optimization, nodes cooperate to minimize an overall objective function that is the sum (or average) of per-node private objective functions. Algorithms interleave local computations with communication among all or a subset of the nodes. Motivated by a variety of applications---distributed estimation in sensor networks, fitting models to massive data sets, and distributed control of multi-robot systems, to name a few---significant advances have been made towards the development of robust, practical algorithms with theoretical performance guarantees. This paper presents an overview of recent work in this area. In general, rates of convergence depend not only on the number of nodes involved and the desired level of accuracy, but also on the structure and nature of the network over which nodes communicate (e.g., whether links are directed or undirected, static or time-varying). We survey the state-of-the-art algorithms and their analyses tailored to these different scenarios, highlighting the role of the network topology. Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... In this paper, we study two related iterative randomized algorithms for distributed computation of averages. The first algorithm is the Broadcast Gossip Algorithm, in which at each iteration one randomly selected node broadcasts its own state to its neighbors. The second algorithm is a novel variation of the former, in which at each iteration every node is allowed to broadcast: hence, this algorithm, which we call Collision Broadcast Gossip Algorithm (CBGA), is affected by interference among messages. The performance of both algorithms is evaluated in terms of rate of convergence and asymptotical error: focusing on large Abelian Cayley networks, we highlight the role of topology and of design parameters. We show that on fully connected graphs the rate of convergence is bounded away from one, whereas the asymptotical error is bounded away from zero. On the contrary, on sparse graphs the rate of convergence goes to one and the asymptotical error goes to zero, as the size of the network grows larger. Our results also show that the performance of the CBGA is close to the performance of the BGA: this indicates the robustness of broadcast gossip algorithms to interferences. Gossiping is a distributed process whose purpose is to enable the members of a group of n>1 autonomous agents to asymptotically determine in a decentralized manner, the average of the initial values of their scalar gossip variables. This paper analyzes the accelerated gossip algorithms, first proposed in Cao, Spielman, and Yeh (2006), in which local memory is exploited by installing shift-registers at each agent. For the two-register case, the existence of the desired convergence is established under a symmetry assumption by separately studying the convergence in expectation and in mean square. In particular, the optimal rate of convergence in expectation is derived which is faster than that of the standard gossip algorithm, and a sufficient condition on the adjustable parameter for the convergence in mean square is provided. These theoretical results are validated for some classes of networks by comparison with existing empirical data. More general multi-register cases are also discussed.