Flooding time in edge-Markovian dynamic graphs

Clementi, Andrea E. F.; Macci, Claudio; Monti, Angelo; Pasquale, Francesco; Silvestri, Riccardo

doi:10.1145/1400751.1400781

Cited by 93 publications

(153 citation statements)

References 21 publications

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“…The time required for global broadcast has been studied in a probabilistic version of the edge-dynamic graph model, where edges are independently formed and removed according to simple Markov processes [10,11,12]. Similar edge-dynamic graphs have also been considered in control theory literature, e.g.…”

Section: Related Workmentioning

confidence: 99%

Distributed computation in dynamic networks

Kühn

Lynch

Oshman

2010

Proceedings of the Forty-Second ACM Symposium on Theory of Computing

317

569

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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 worst-case 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 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 T -interval connectivity (for T ≥ 1), which stipulates that for every T consecutive rounds there exists a stable connected spanning subgraph. For T = 1 this means that the graph is connected in every round, but changes arbitrarily between rounds.We show that in 1-interval connected graphs it is possible for nodes to determine the size of the network and compute any computable function of their initial inputs in O(n 2 ) rounds using messages of size O(log n + d), where d is the size of the input to a single node. Further, if the graph is T -interval connected for T > 1, the computation can be sped up by a factor of T , and any function can be computed in O(n + n 2 /T ) rounds using messages of size O(log n + d). We also give two lower bounds on the token dissemination problem, which requires the nodes to disseminate k pieces of information to all the nodes in the network.The T-interval connected dynamic graph model is a novel model, which we believe opens new avenues for research in the theory of distributed computing in wireless, mobile and dynamic networks.

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Section: Related Workmentioning

confidence: 99%

Distributed computation in dynamic networks

Kühn

Lynch

Oshman

2010

Proceedings of the Forty-Second ACM Symposium on Theory of Computing

317

569

View full text Add to dashboard Cite

show abstract

“…This problem has already been addressed by researchers studying epidemic dissemination in mobile systems [17]: nonetheless, their temporal analysis of message spreading usually exploits either mean-field approximation to study their behavior in the limit of large systems [18]. Some attempts have also focused on providing tight bounds on the speed of information dissemination on Markovian time-varying graphs [19]. These solutions provide good estimation of steady state behavior of the system, but can be misleading when they are used to analyze the transient behavior of the first steps of the dissemination.…”

Section: Temporal Random Network Modelmentioning

confidence: 99%

Evaluating Temporal Robustness of Mobile Networks

Scellato

Leontiadis

Mascolo

et al. 2013

IEEE Trans. on Mobile Comput.

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Abstract-The application of complex network models to communication systems has led to several important results: nonetheless, previous research has often neglected to take into account their temporal properties, which in many real scenarios play a pivotal role. At the same time, network robustness has come extensively under scrutiny. Understanding whether networked systems can undergo structural damage and yet perform efficiently is crucial to both their protection against failures and to the design of new applications. In spite of this, it is still unclear what type of resilience we may expect in a network which continuously changes over time. In this work we present the first attempt to define the concept of temporal network robustness: we describe a measure of network robustness for time-varying networks and we show how it performs on different classes of random models by means of analytical and numerical evaluation. Finally, we report a case study on a real-world scenario, an opportunistic vehicular system of about 500 taxicabs, highlighting the importance of time in the evaluation of robustness. Particularly, we show how static approximation can wrongly indicate high robustness of fragile networks when adopted in mobile time-varying networks, while a temporal approach captures more accurately the system performance.

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“…This issue is distinct from network growth, or aggregative phenomena: it embodies the property that all edges within the network are transient to some extent. Very recently, general classes of dynamic networks have been proposed and studied in the theoretical computer science literature (Avin et al 2008;Clementi et al 2008Clementi et al , 2009) from a complexity theory perspective. Our work looks at complementary issues driven by the need for practical tools in modelling, calibration and data analysis.…”

Section: Introductionmentioning

confidence: 99%

Evolving graphs: dynamical models, inverse problems and propagation

Grindrod

Higham

2009

Proc. R. Soc. A.

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Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

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Flooding time in edge-Markovian dynamic graphs

Cited by 93 publications

References 21 publications

Distributed computation in dynamic networks

Distributed computation in dynamic networks

Evaluating Temporal Robustness of Mobile Networks

Evolving graphs: dynamical models, inverse problems and propagation

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