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Analyzing Network Coding Gossip Made Easy
, 2011
"... We introduce projection analysis – a new technique to analyze the stopping time of gossip protocols that are based on random linear network coding (RLNC). Projection analysis drastically simplifies, extends and strengthens previous results. We analyze RLNC gossip in a general framework for network a ..."
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Cited by 15 (8 self)
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We introduce projection analysis – a new technique to analyze the stopping time of gossip protocols that are based on random linear network coding (RLNC). Projection analysis drastically simplifies, extends and strengthens previous results. We analyze RLNC gossip in a general framework for network and communication models that encompasses and unifies the models used previously in this context. We show, in most settings for the first time, that the RLNC gossip converges with high probability in optimal time. Most stopping times are of the form O(k + T), where k is the number of messages to be distributed and T is the time it takes to disseminate one message. This means RLNC gossip achieves “perfect pipelining”. Our analysis directly extends to highly dynamic networks in which the topology can change completely at any time. This remains true, even if the network dynamics are controlled by a fully adaptive adversary that knows the complete network state. Virtually nothing besides simple O(kT) sequential flooding protocols was previously known for such a setting. While RLNC gossip works in this wide variety of networks our analysis remains the same and extremely simple. This contrasts with more complex proofs that were put forward to give less strong results for various special cases.
Parsimonious flooding in dynamic graphs
 In Proc. of 28th Symp. on Principles of Distributed Computing (PODC
, 2009
"... An edgeMarkovian process with birthrate p and deathrate q generates sequences of graphs (G0, G1, G2,...) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e / ∈ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e / ∈ E(Gt) with probability q. Clementi e ..."
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Cited by 15 (1 self)
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An edgeMarkovian process with birthrate p and deathrate q generates sequences of graphs (G0, G1, G2,...) with the same node set [n] such that Gt is obtained from Gt−1 as follows: if e / ∈ E(Gt−1) then e ∈ E(Gt) with probability p, and if e ∈ E(Gt−1) then e / ∈ E(Gt) with probability q. Clementi et al. (PODC 2008) analyzed thoroughly information dissemination in such dynamic graphs, by establishing bounds on their flooding time — flooding is the basic mechanism in which every node becoming aware of an information at step t forwards this information to all its neighbors at all forthcoming steps t ′> t. In this paper, we establish tight bounds on the complexity of flooding for all possible birth rates and death rates, completing the previous results by Clementi et al. Moreover, we note that despite its many advantages in term of simplicity and robustness, flooding suffers from its high bandwidth consumption. Hence we al! so show that flooding in dynamic graphs can be implemented in a more parsimonious manner, so that to save bandwidth, yet preserving efficiency in term of simplicity and completion time. For a positive integer k, we say that the flooding protocol is kactive if each node forwards an information only during the k time steps immediately following the step at which the node receives that information for the first time. We define the reachability threshold for the flooding protocol as the smallest integer k such that, for any source s ∈ [n], the kactive flooding protocol from s completes (i.e., reaches all nodes), and we establish tight bounds for this parameter. We show that, for a large spectrum of parameters p and q, the reachability threshold is by several orders of magnitude smaller than the flooding time. In particular, we show A part of this work was done during the stay of the second
Information Dissemination via Gossip: Applications to Averaging and Coding”. available at http:// www.arXiv.org /cs.NI/0504029
"... We study distributed algorithms, also known as gossip algorithms, for information dissemination in an arbitrary connected network of nodes. Distributed algorithms have applications to peertopeer, sensor, and ad hoc networks, in which nodes operate under limited computational, communication, and en ..."
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Cited by 14 (2 self)
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We study distributed algorithms, also known as gossip algorithms, for information dissemination in an arbitrary connected network of nodes. Distributed algorithms have applications to peertopeer, sensor, and ad hoc networks, in which nodes operate under limited computational, communication, and energy resources. These constraints naturally give rise to “gossip” algorithms: schemes in which nodes repeatedly communicate with randomly chosen neighbors, thus distributing the computational burden across all the nodes in the network. We analyze the information dissemination problem under the gossip constraint for arbitrary networks, and find that the information dissemination time of a gossip algorithm is strongly related to the isoperimetric properties of the underlying graph. This characterization allows us to formulate the problem of finding the fastest information dissemination algorithm as a concave maximization problem over the convex set of graphconformant doubly stochastic matrices. Next, we use these results for two seemingly unrelated important questions: distributed averaging and coding based information dissemination. For averaging, we analyze an algorithm based on a classic result of Flajolet and Martin [7]. Information dissemination based on coding was introduced by Deb and Médard [6]. They showed the virtue of coding by analyzing a coding algorithm for a complete graph. Although their scheme generalizes to arbitrary graphs, the analysis does not. We present an analysis of this algorithm for arbitrary graphs, which suggests that for a large class of graphs, such as gridlike graphs, codingbased algorithms do not seem to improve performance. Finally, we apply our results to several classes of graphs: complete graphs, expander graphs, and grid graphs. 1
Gossip and Mixing Times of Random Walks on Random Graphs
, 2004
"... 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 algo ..."
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Cited by 13 (0 self)
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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...
Distributed algorithms for constructing approximate minimum spanning trees with applications to wireless sensor networks
 THE IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS (TPDS). HTTP://WWW.CS.PURDUE.EDU/HOMES/MMKHAN/PAPERS/TPDS.PDF
"... The Minimum Spanning Tree (MST) problem is an important and commonly occurring primitive in the design and operation of data and communication networks. While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time, and are fairly i ..."
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Cited by 12 (5 self)
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The Minimum Spanning Tree (MST) problem is an important and commonly occurring primitive in the design and operation of data and communication networks. While there are distributed algorithms for the MST problem, these algorithms require relatively large number of messages and time, and are fairly involved, require synchronization and a lot of book keeping; this makes these algorithms impractical for resourceconstrained networks such as ad hoc wireless sensor networks. In such networks, a sensor has very limited power, and any algorithm needs to be simple, local, and energy efficient for being practical. Motivated by these considerations, we design and analyze a class of simple and local distributed algorithms called Nearest Neighbor Tree (NNT) algorithms for energyefficient construction of MSTs in a wireless ad hoc setting. We assume that the nodes are uniformly distributed in a unit square and show provable bounds on the performance with respect to both the quality of the spanning tree produced and the energy needed to construct them. In particular, we show that NNT produces a close approximation to the MST, and they can be maintained dynamically with polylogarithmic number of rearrangements under node insertions/deletions. We also perform extensive simulations of our algorithms. We tested our algorithms on both uniformly random distributions of nodes, and on a realistic distributions of nodes in an urban setting. Simulations validate
Formal Analysis Techniques for Gossiping Protocols
 ACM SIGOPS Oper. Syst. Rev.
, 2007
"... 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 the ..."
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Cited by 11 (4 self)
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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.
Tools for Large Graph Mining
, 2005
"... by a gift from NorthropGrumman Corporation. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity. ..."
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Cited by 10 (1 self)
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by a gift from NorthropGrumman Corporation. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.
Robust gossiping with an application to consensus
 Journal of Computer and System Sciences
"... 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, ..."
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Cited by 9 (5 self)
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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 nonfaulty. We show a tradeoff 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.
Fast Information Spreading in Graphs with Large Weak Conductance
"... Gathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider information spreading among n nodes of a network, where each node v has a message m(v) which must be received by all other nodes. The time required for i ..."
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Cited by 8 (1 self)
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Gathering data from nodes in a network is at the heart of many distributed applications, most notably, while performing a global task. We consider information spreading among n nodes of a network, where each node v has a message m(v) which must be received by all other nodes. The time required for information spreading has been previously upperbounded with an inverse relationship to the conductance of the underlying communication graph. This implies high running times for graphs with small conductance. The main contribution of this paper is an information spreading algorithm which overcomes communication bottlenecks and thus achieves fast information spreading for a wide class of graphs, despite their small conductance. As a key tool in our study we use the recently defined concept of