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48
GossipBased Computation of Aggregate Information
, 2003
"... 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 gossipbased protocols are emergin ..."
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Cited by 297 (1 self)
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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 gossipbased protocols are emerging as an approach to maintaining simplicity and scalability while achieving faulttolerant information dissemination.
Randomized Gossip Algorithms
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2006
"... Motivated by applications to sensor, peertopeer, 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 a ..."
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Cited by 208 (5 self)
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Motivated by applications to sensor, peertopeer, 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 socalled Preferential Connectivity (PC) model.
Spatial gossip and resource location protocols
, 2001
"... 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 d ..."
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Cited by 141 (7 self)
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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 distancebased 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
Algebraic gossip: A network coding approach to optimal multiple rumor mongering
 IEEE Transactions on Information Theory
, 2004
"... 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 mo ..."
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Cited by 78 (11 self)
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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 discretetime steps, and in every timestep, 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 timestep, 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 gossipbased 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
Computing separable functions via gossip
 In Proceedings of the TwentyFifth Annual ACM Symposium on Principles of Distributed Computing (PODC
, 2006
"... Motivated by applications to sensor, peertopeer, and adhoc 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 or products of function ..."
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Cited by 48 (6 self)
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Motivated by applications to sensor, peertopeer, and adhoc 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 or products of functions of individual variables. The main contribution of this paper is the design of a distributed 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 a characterization of the information spreading time of the gossip algorithm, and therefore the computation time for separable functions, in terms of the conductance of an appropriate stochastic matrix. Specifically, we find that for a class of graphs with small spectral gap, this time is of a smaller order than the time required to compute averages for a known iterative gossip scheme [4]. 1
Correctness of a gossip based membership protocol
 in Proceedings of the twentyfourth annual ACM symposium on Principles of distributed computing, ser. PODC ’05
, 1990
"... The importance of scalability and faulttolerance in modern distributed systems has led to considerable research in multicast protocols using gossip. In a gossip protocol, each node forwards messages to a small set of “gossip partners ” chosen at random from the entire group membership. By discardin ..."
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Cited by 46 (0 self)
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The importance of scalability and faulttolerance in modern distributed systems has led to considerable research in multicast protocols using gossip. In a gossip protocol, each node forwards messages to a small set of “gossip partners ” chosen at random from the entire group membership. By discarding the strong reliability guarantees of traditional protocols in favour of probabilistic guarantees, gossip protocols can deliver greater scalability and fault tolerance. In early gossip algorithms, partners were chosen uniformly at random from the entire membership, limiting scalability because of the resources required to store and maintain complete membership views at each node. Later protocols avoided this issue by storing much smaller random subsets of the membership at each node, and choosing gossip partners only from these local views. Such protocols are subtle: at least some local views must change in response to group membership changes in order to preserve connectivity and performance guarantees. While these protocols have been the subject of much simulation and analysis, formal proofs of key properties – in particular the probability of partitioning – have remained elusive. In this paper we give a new scalable gossipbased algorithm for local view maintenance, together with a proof that the expected time until a network partition is at least exponential in the square of the view size. We also develop probabilistic bounds on the indegree (hence the load) of individual nodes, and argue that protocols lacking our reinforcement component eventually converge to starlike networks, whose connectivity depends on a small set of overloaded nodes. We also argue that the undirected connectivity graph is an expander, for which applicationlevel gossip multicast protocols will converge rapidly. Our theoretical results are supported by simulations.
Distributed Computation in Dynamic Networks
, 2009
"... In this paper we investigate distributed computation in dynamic networks in which the network topology changes from round to round. We consider a worstcase 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 rou ..."
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Cited by 33 (7 self)
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In this paper we investigate distributed computation in dynamic networks in which the network topology changes from round to round. We consider a worstcase 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
Fast distributed algorithms for computing separable functions
 IEEE Trans. Inform. Theory
"... 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, peertopeer, and adhoc networks. The task of computing separable f ..."
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Cited by 27 (5 self)
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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, peertopeer, 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.
Spatiallydecaying aggregation over a network: model and algorithms
 In SIGMOD. ACM
, 1999
"... Data items are often associated with a location in which they are present or collected, and their relevance or influence decays with their distance. Aggregate values over such data thus depend on the observing location, where the weight given to each item depends on its distance from that location. ..."
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Cited by 24 (8 self)
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Data items are often associated with a location in which they are present or collected, and their relevance or influence decays with their distance. Aggregate values over such data thus depend on the observing location, where the weight given to each item depends on its distance from that location. We term such aggregation spatiallydecaying. Spatiallydecaying aggregation has numerous applications: Individual sensor nodes collect readings of an environmental parameter such as contamination level or parking spot availability; the nodes then communicate to integrate their readings so that each location obtains contamination level or parking availability in its neighborhood. Nodes in a p2p network could use a summary of content and properties of nodes in their neighborhood in order to guide search. In graphical databases such as Web hyperlink structure, properties such as subject of pages that can reach or be reached from a page using link traversals provide information on the page. We formalize the notion of spatiallydecaying aggregation and develop efficient algorithms for fundamental aggregation functions, including sums and averages, random sampling, heavy hitters, quantiles, and norms. 1
Timevarying graphs and dynamic networks
 International Journal of Parallel, Emergent and Distributed Systems
"... The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems – delaytolerant networks, opportunisticmobility networks, social networks – obtaining closely related insights. Indeed, the concepts discovered in these investigations can be v ..."
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Cited by 20 (8 self)
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The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems – delaytolerant networks, opportunisticmobility networks, social networks – obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe; and the formal models proposed so far to express some specific concepts are components of a larger formal description of this universe. The main contribution of this paper is to integrate the vast collection of concepts, formalisms, and results found in the literature into a unified framework, which we call TVG (for timevarying graphs). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. Based on this definitional work, employing both existing results and original observations, we present a hierarchical classification of TVGs; each class corresponds to a significant property examined in the distributed computing literature. We then examine how TVGs can be used to study the evolution of network properties, and propose different techniques, depending on whether the indicators for these properties are atemporal (as in the majority of existing studies) or temporal. Finally, we briefly discuss the introduction of randomness in TVGs.