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Rumor Spreading in Random Evolving Graphs

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Algorithms – ESA 2013 (ESA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8125))

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Abstract

In this paper, we aim at analyzing the classical information spreading push protocol in dynamic networks. We consider the edge-Markovian evolving graph model which captures natural temporal dependencies between the structure of the network at time t, and the one at time t + 1. Precisely, a non-edge appears with probability p, while an existing edge dies with probability q. In order to fit with real-world traces, we mostly concentrate our study on the case where \(p=\Omega(\frac{1}{n})\) and q is constant. We prove that, in this realistic scenario, the push protocol does perform well, completing information spreading in O(logn) time steps, w.h.p., even when the network is, w.h.p., disconnected at every time step (e.g., when \(p\ll \frac{\log n}{n}\)). The bound is tight. We also address other ranges of parameters p and q (e.g., p + q = 1 with arbitrary p and q, and \(p=\Theta\left(\frac{1}{n}\right)\) with arbitrary q). Although they do not precisely fit with the measures performed on real-world traces, they can be of independent interest for other settings. The results in these cases confirm the positive impact of dynamism.

A. Clementi is supported by Italian MIUR under the COFIN 2010-11 project ARS TechnoMedia. C. Doerr is supported by a F. Lynen postdoctoral research fellowship of the A. von Humboldt Foundation and by ANR project CRYQ. P. Fraigniaud is supported by ANR project DISPLEXITY, and INRIA project GANG. A. Panconesi is supported by a Google Faculty Research Award and EU FET project MULTIPLEX 317532. F. Pasquale is supported by EU FET project MULTIPLEX 317532.

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Author information

Authors and Affiliations

  1. Università Tor Vergata di Roma, Italy

    Andrea Clementi

  2. Università di Firenze, Italy

    Pierluigi Crescenzi

  3. Université Paris Diderot and Max Planck Institute Saarbrücken, Germany

    Carola Doerr

  4. CNRS and Université Paris Diderot, France

    Pierre Fraigniaud

  5. Sapienza Università di Roma, Italy

    Marco Isopi, Alessandro Panconesi, Francesco Pasquale & Riccardo Silvestri

Authors
  1. Andrea Clementi
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  2. Pierluigi Crescenzi
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  3. Carola Doerr
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  4. Pierre Fraigniaud
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  5. Marco Isopi
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  6. Alessandro Panconesi
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  7. Francesco Pasquale
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  8. Riccardo Silvestri
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Rome, Italy

    Giuseppe F. Italiano

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Clementi, A. et al. (2013). Rumor Spreading in Random Evolving Graphs. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_28

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  • DOI: https://doi.org/10.1007/978-3-642-40450-4_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40449-8

  • Online ISBN: 978-3-642-40450-4

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