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Total Flooding Time and Rumor Propagation on Graphs

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Abstract

We study the discrete time version of the flooding time problem as a model of rumor propagation where each site in the graph has initially a distinct piece of information; we are interested in the number of “conversations” before the entire graph knows all pieces of information. For the complete graph we compare the ratio between the expected propagation time for all pieces of information and the corresponding time for a single piece of information, obtaining the asymptotic ratio 3 / 2 between them.

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Acknowledgements

We would like to thank both referees for their helpful and detailed reports that assisted us in finishing this work and especially the second referee for the answer to our former open problem, which is now Theorem 1.5.

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Authors and Affiliations

  1. Department of Statistics, Institute of Mathematics, Statistics and Scientific Computation, University of Campinas – UNICAMP, rua Sérgio Buarque de Holanda 651, 13083–859, Campinas, SP, Brazil

    Darcy Camargo & Serguei Popov

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  1. Darcy Camargo
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  2. Serguei Popov
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Correspondence to Darcy Camargo.

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Funding

This work was supported by the Brazilian founding agencies FAPESP (Grant Number 2013/23081-6).

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Camargo, D., Popov, S. Total Flooding Time and Rumor Propagation on Graphs. J Stat Phys 166, 1558–1571 (2017). https://doi.org/10.1007/s10955-017-1731-0

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  • DOI: https://doi.org/10.1007/s10955-017-1731-0

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