Almost-Optimal Gossip-Based Aggregate Computation

Chen, Jen-Yeu; Pandurangan, Gopal

doi:10.1137/100793104

Cited by 16 publications

(23 citation statements)

References 20 publications

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“…Feige [24,23] showed that the cover time of a random walk on any undirected n-node connected graph is between Θ(n log n) and Θ(n 3 ) with both the lower and upper bounds being achieved in certain graphs. With the rapidly increasing interest in information (rumor) spreading processes in largescale networks and the gossiping paradigm (e.g., see [9] and the references therein), there have been a number of studies on speeding up the cover time of random walks on graphs.…”

Section: Related Work and Comparisonmentioning

confidence: 99%

Coalescing-branching random walks on graphs

Dutta

Pandurangan

Rajaraman

et al. 2013

Proceedings of the Twenty-Fifth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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We study a distributed randomized information propagation mechanism in networks we call the coalescing-branching random walk (cobra walk, for short). A cobra walk is a generalization of the well-studied "standard" random walk, and is useful in modeling and understanding the SusceptibleInfected-Susceptible (SIS)-type of epidemic processes in networks. It can also be helpful in performing light-weight information dissemination in resource-constrained networks. A cobra walk is parameterized by a branching factor k. The process starts from an arbitrary node, which is labeled active for step 1. (For instance, this could be a node that has a piece of data, rumor, or a virus.) In each step of a cobra walk, each active node chooses k random neighbors to become active for the next step ("branching"). A node is active for step t + 1 only if it is chosen by an active node in step t ("coalescing"). This results in a stochastic process in the underlying network with properties that are quite different from both the standard random walk (which is equivalent * Chinmoy ...$15.00.to the cobra walk with branching factor 1) as well as other gossip-based rumor spreading mechanisms.We focus on the cover time of the cobra walk, which is the number of steps for the walk to reach all the nodes, and derive almost-tight bounds for various graph classes. Our main technical result is an O(log 2 n) high probability bound for the cover time of cobra walks on expanders, if either the expansion factor or the branching factor is sufficiently large; we also obtain an O(log n) high probability bound for the partial cover time, which is the number of steps needed for the walk to reach at least a constant fraction of the nodes. We show that the cobra walk takes O(n log n) steps on any n-node tree for k ≥ 2, andÕ(n 1/d ) steps on a d-dimensional grid for k ≥ 2, with high probability.

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Section: Related Work and Comparisonmentioning

confidence: 99%

Coalescing-branching random walks on graphs

Dutta

Pandurangan

Rajaraman

et al. 2013

Proceedings of the Twenty-Fifth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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“…In particular, gossip‐based protocols have been used to efficiently and robustly construct various overlay topologies dynamically in a fully decentralized manner . In a local gossip‐based algorithm (e.g., ), each node exchanges information with a small number of randomly chosen neighbors in each round . The randomness inherent in the gossip‐based protocols naturally provides robustness, simplicity, and scalability.…”

Section: Introductionmentioning

confidence: 99%

Discovery Through Gossip

Haeupler

Pandurangan

Peleg³

et al. 2016

Random Struct Algorithms

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We study randomized gossip‐based processes in dynamic networks that are motivated by information discovery in large‐scale distributed networks such as peer‐to‐peer and social networks. A well‐studied problem in peer‐to‐peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self‐stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying network — new edges are added to the network — and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications. This paper studies and analyzes two natural gossip‐based discovery processes. In the push discovery or triangulation process, each node repeatedly chooses two random neighbors and connects them (i.e., “pushes” their mutual information to each other). In the pull discovery process or the two‐hop walk, each node repeatedly requests or “pulls” a random contact from a random neighbor and connects itself to this two‐hop neighbor. Both processes are lightweight in the sense that the amortized work done per node is constant per round, local, and naturally robust due to the inherent randomized nature of gossip. Our main result is an almost‐tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n‐node graph both processes take O(nlog2n) rounds to connect every node to all other nodes with high probability, whereas Ω(nlogn) is a lower bound. We also study the two‐hop walk in directed graphs, and show that it takes O(n2logn) time with high probability, and that the worst‐case bound is tight for arbitrary directed graphs, whereas Ω(n2) is a lower bound for strongly connected directed graphs. A key technical challenge that we overcome in our work is the analysis of a randomized process that itself results in a constantly changing network leading to complicated dependencies in every round. We discuss implications of our results and their analysis to discovery problems in P2P networks as well as to evolution in social networks. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 48, 565–587, 2016

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“…In this paper, we study the dynamics of network evolution that result from local gossip-style processes. Gossip-based processes have recently received significant attention because of their simplicity of implementation, scalability to large network size, and robustness to frequent network topology changes; see, e.g., [8,11,13,19,[27][28][29][30][31]35] and the references therein. In particular, gossip-based protocols have been used to efficiently and robustly construct various overlay topologies dynamically in a fully decentralized manner [27].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, gossip-based protocols have been used to efficiently and robustly construct various overlay topologies dynamically in a fully decentralized manner [27]. In a local gossip-based algorithm (e.g., [13]), each node exchanges information with a small number of randomly chosen neighbors in each round. 1 The randomness inherent in the gossip-based protocols naturally provides robustness, simplicity, and scalability.…”

Section: Introductionmentioning

confidence: 99%

“…1 The randomness inherent in the gossip-based protocols naturally provides robustness, simplicity, and scalability. While many of the theoretical gossip-based work (including those on rumor spreading), especially, the push-pull type algorithms [13,14,22,23,28,29] focus on analyzing various gossip-based tasks (e.g., computing aggregates or spreading a rumor) on static graphs, a key feature of this work is rigorously analyzing a gossip-based process in a dynamically changing graph, where the graph topology changes in a probabilistic fashion due to the behaviour of the gossip-style process itself. We also note that there have been recent works (see e.g., [4-7, 15-17, 24, 37] and the references therein) that have analyzed gossip-style processes, random walks, and flooding processes in dynamic networks where the topological changes are determined by an adversary (usually, but not always, independent of the processes that occur over these networks).…”

Section: Introductionmentioning

confidence: 99%

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Discovery through gossip

Haeupler

Pandurangan²,

Peleg

et al. 2012

Proceedings of the Twenty-Fourth Annual ACM Symposium on Parallelism in Algorithms and Architectures

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We study randomized gossip-based processes in dynamic networks that are motivated by information discovery in large-scale distributed networks such as peer-to-peer and social networks. A well-studied problem in peer-to-peer networks is resource discovery, where the goal for nodes (hosts with IP addresses) is to discover the IP addresses of all other hosts. Also, some of the recent work on self-stabilization algorithms for P2P/overlay networks proceed via discovery of the complete network. In social networks, nodes (people) discover new nodes through exchanging contacts with their neighbors (friends). In both cases the discovery of new nodes changes the underlying networknew edges are added to the network -and the process continues in the changed network. Rigorously analyzing such dynamic (stochastic) processes in a continuously changing topology remains a challenging problem with obvious applications. 566HAEUPLER ET AL.This paper studies and analyzes two natural gossip-based discovery processes. In the push discovery or triangulation process, each node repeatedly chooses two random neighbors and connects them (i.e., "pushes" their mutual information to each other). In the pull discovery process or the two-hop walk, each node repeatedly requests or "pulls" a random contact from a random neighbor and connects itself to this two-hop neighbor. Both processes are lightweight in the sense that the amortized work done per node is constant per round, local, and naturally robust due to the inherent randomized nature of gossip.Our main result is an almost-tight analysis of the time taken for these two randomized processes to converge. We show that in any undirected n-node graph both processes take O(n log 2 n) rounds to connect every node to all other nodes with high probability, whereas (n log n) is a lower bound. We also study the two-hop walk in directed graphs, and show that it takes O(n 2 log n) time with high probability, and that the worst-case bound is tight for arbitrary directed graphs, whereas (n 2 ) is a lower bound for strongly connected directed graphs. A key technical challenge that we overcome in our work is the analysis of a randomized process that itself results in a constantly changing network leading to complicated dependencies in every round. We discuss implications of our results and their analysis to discovery problems in P2P networks as well as to evolution in social networks.

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Almost-Optimal Gossip-Based Aggregate Computation

Cited by 16 publications

References 20 publications

Coalescing-branching random walks on graphs

Coalescing-branching random walks on graphs

Discovery Through Gossip

Discovery through gossip

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