Rumor Spreading with Bounded In-Degree

Daum, Sebastian; Kühn, Fabian

doi:10.1007/978-3-319-48314-6_21

Cited by 20 publications

(22 citation statements)

References 21 publications

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“…Whether there exists any distributed rumor spreading algorithm that can approach optimal bounds with respect to vertex expansion under these assumptions, however, remains an intriguing open question. For the case of graph conductance, we note that a consequence of a result from [4] is that PUSH-PULL in this setting comes within a log factor of the (slow) O( ∆ δ·φ log n) optimal bound proved in Section 5. In other words, in the mobile telephone model rumor spreading might be slow with respect to a graph's conductance, but PUSH-PULL matches this slow spreading time.…”

Section: Resultsmentioning

confidence: 76%

“…They study a restricted model in which each node can only accept a single connection per round. We emphasize that the mobile telephone model with b = 0 and τ = ∞ is equivalent to the model of [4]. 2 This existing work proves the existence of graphs where PULL works in polylogarithmic time in the classical telephone model but requires Ω( √ n) rounds in their bounded variation.…”

Section: Related Workmentioning

confidence: 77%

“…Recent work by Daum et al [4] emphasized the shortcoming of the telephone model mentioned above: it allows a single node to accept an unlimited number of incoming connections. They study a restricted model in which each node can only accept a single connection per round.…”

Section: Related Workmentioning

confidence: 99%

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How to Discreetly Spread a Rumor in a Crowd

Ghaffari¹,

Newport

2016

Lecture Notes in Computer Science

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In this paper, we study PUSH-PULL style rumor spreading algorithms in the mobile telephone model, a variant of the classical telephone model in which each node can participate in at most one connection per round; i.e., you can no longer have multiple nodes pull information from the same source in a single round. Our model also includes two new parameterized generalizations: (1) the network topology can undergo a bounded rate of change (for a parameterized rate that spans from no changes to changes in every round); and (2) in each round, each node can advertise a bounded amount of information to all of its neighbors before connection decisions are made (for a parameterized number of bits that spans from no advertisement to large advertisements). We prove that in the mobile telephone model with no advertisements and no topology changes, PUSH-PULL style algorithms perform poorly with respect to a graph's vertex expansion and graph conductance as compared to the known tight results in the classical telephone model. We then prove, however, that if nodes are allowed to advertise a single bit in each round, a natural variation of PUSH-PULL terminates in time that matches (within logarithmic factors) this strategy's performance in the classical telephone model-even in the presence of frequent topology changes. We also analyze how the performance of this algorithm degrades as the rate of change increases toward the maximum possible amount. We argue that our model matches well the properties of emerging peer-to-peer communication standards for mobile devices, and that our efficient PUSH-PULL variation that leverages small advertisements and adapts well to topology changes is a good choice for rumor spreading in this increasingly important setting.

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Section: Resultsmentioning

confidence: 76%

Section: Related Workmentioning

confidence: 77%

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How to Discreetly Spread a Rumor in a Crowd

Ghaffari¹,

Newport

2016

Lecture Notes in Computer Science

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“…Another issue is whether we can reduce the number of incoming messages in a round; recently, Daum et al [9] have considered such a more restricted model, yielding interesting results. It would also be interesting to look at the bounds where each node is only allowed O(1) connections per round, whether initiated by the node itself or by its neighbor.…”

Section: Resultsmentioning

confidence: 99%

Slow Links, Fast Links, and the Cost of Gossip

Sourav

Robinson

Gilbert

2018

2018 IEEE 38th International Conference on Distributed Computing Systems (ICDCS)

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Consider the classical problem of information dissemination: one (or more) nodes in a network have some information that they want to distribute to the remainder of the network. In this paper, we study the cost of information dissemination in networks where edges have latencies, i.e., sending a message from one node to another takes some amount of time. We first generalize the idea of conductance to weighted graphs by defining φ * to be the "critical conductance" and * to be the "critical latency". One goal of this paper is to argue that φ * characterizes the connectivity of a weighted graph with latencies in much the same way that conductance characterizes the connectivity of unweighted graphs.We give near tight lower and upper bounds on the problem of information dissemination, up to polylogarithmic factors. Specifically, we show that in a graph with (weighted) diameter D (with latencies as weights) and maximum degree ∆, any information dissemination algorithm requires at least Ω(min(D+ ∆, * /φ * )) time in the worst case. We show several variants of the lower bound (e.g., for graphs with small diameter, graphs with small max-degree, etc.) by reduction to a simple combinatorial game.We then give nearly matching algorithms, showing that information dissemination can be solved in O(min((D + ∆) log 3 n, ( * /φ * ) log n) time. This is achieved by combining two cases. We show that the classical push-pull algorithm is (near) optimal when the diameter or the maximum degree is large. For the case where the diameter and the maximum degree are small, we give an alternative strategy in which we first discover the latencies and then use an algorithm for known latencies based on a weighted spanner construction. (Our algorithms are within polylogarithmic factors of being tight both for known and unknown latencies.)While it is easiest to express our bounds in terms of φ * and * , in some cases they do not provide the most convenient definition of conductance in weighted graphs. Therefore we give a second (nearly) equivalent characterization, namely the average conductance φ avg . arXiv:1611.06343v3 [cs.DC] 17 Dec 2018Consider the problem of disseminating information in a large-scale distributed system: a source node in the network has some information that it wants to share/aggregate/reconcile with others. This fundamental problem has been widely studied under various names, e.g., information dissemination (e.g., [5]), rumor spreading (e.g., [8]), global broadcast (e.g., [20]), one-to-all multicast, information spreading (e.g., [6]), and gossip (e.g., [21]).Real world network communication often has a time delay, which we model here as edges with latencies. The latency of an edge captures how long communication takes, i.e., how many rounds it takes for two neighbors to exchange information. Low latency on links imply faster message transmission whereas higher latency implies longer delays.In the case of unweighted graphs, all edges are considered the same and are said to have unit latencies. However, this is not true in real...

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“…BlindMatch O((1/α)k∆ 2 log 2 n) b = 1, τ ≥ 1 SharedBit* O(kn) b = 1, τ ≥ 1 SimSharedBit** O(kn + (1/α)∆ 1/τ log 6 Figure 1: A summary of gossip and ǫ-gossip round complexity bounds proved in this paper. (In the ǫ-gossip problem, it is assumed that every node starts with a message, but each node need only learn an ǫfraction of the n total messages.)…”

Section: Assumptions Algorithmmentioning

confidence: 90%

Gossip in a Smartphone Peer-to-Peer Network

Newport

2017

Proceedings of the ACM Symposium on Principles of Distributed Computing

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In this paper, we study the fundamental problem of gossip in the mobile telephone model: a recently introduced variation of the classical telephone model modified to better describe the local peer-to-peer communication services implemented in many popular smartphone operating systems. In more detail, the mobile telephone model differs from the classical telephone model in three ways: (1) each device can participate in at most one connection per round; (2) the network topology can undergo a parameterized rate of change; and (3) devices can advertise a parameterized number of bits about their state to their neighbors in each round before connection attempts are initiated. We begin by describing and analyzing new randomized gossip algorithms in this model under the harsh assumption of a network topology that can change completely in every round. We prove a significant time complexity gap between the case where nodes can advertise 0 bits to their neighbors in each round, and the case where nodes can advertise 1 bit. For the latter assumption, we present two solutions: the first depends on a shared randomness source, while the second eliminates this assumption using a pseudorandomness generator we prove to exist with a novel generalization of a classical result from the study of two-party communication complexity. We then turn our attention to the easier case where the topology graph is stable, and describe and analyze a new gossip algorithm that provides a substantial performance improvement for many parameters. We conclude by studying a relaxed version of gossip in which it is only necessary for nodes to each learn a specified fraction of the messages in the system. We prove that our existing algorithms for dynamic network topologies and a single advertising bit solve this relaxed version up to a polynomial factor faster (in network size) for many parameters. These are the first known gossip results for the mobile telephone model, and they significantly expand our understanding of how to communicate and coordinate in this increasingly relevant setting.

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Rumor Spreading with Bounded In-Degree

Cited by 20 publications

References 21 publications

How to Discreetly Spread a Rumor in a Crowd

How to Discreetly Spread a Rumor in a Crowd

Slow Links, Fast Links, and the Cost of Gossip

Gossip in a Smartphone Peer-to-Peer Network

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