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The Expected Duration of Sequential Gossiping

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Multi-Agent Systems and Agreement Technologies (EUMAS 2017, AT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10767))

Abstract

A gossip protocol aims at arriving, by means of point-to-point communications (or telephone calls), at a situation in which every agent knows all the information initially present in the network. If it is forbidden to have more than one call at the same time, the protocol is called sequential. We generalise a method, that originates from the famous coupon collector’s problem and that was proposed by John Haigh in 1981, for bounding the expected duration of sequential gossip protocols. We give two examples of protocols where this method succeeds and two examples of protocols where this method fails to give useful bounds. Our main contribution is that, although Haigh originally applied this method in a protocol where any call is available at any moment, we show that this method can be applied in protocols where the number of available calls is decreasing. Furthermore, for one of the protocols where Haigh’s method fails we were able to obtain lower bounds for the expectation using results from random graph theory.

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Acknowledgements

We acknowledge financial support from ERC project EPS 313360. We are also grateful to Aris Pagourtzis for useful discussions.

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Authors and Affiliations

  1. CNRS, LORIA, University of Lorraine, Nancy, France

    Hans van Ditmarsch

  2. ReLaX UMI 2000, IMSc, Chennai, India

    Hans van Ditmarsch

  3. TU Dortmund University, Dortmund, Germany

    Ioannis Kokkinis

Authors
  1. Hans van Ditmarsch
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  2. Ioannis Kokkinis
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Corresponding author

Correspondence to Ioannis Kokkinis .

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Editors and Affiliations

  1. University of Évry Val d'Essonne, Paris Saclay, France

    Francesco Belardinelli

  2. Polytechnic University of Valencia, Valencia, Spain

    Estefanía Argente

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van Ditmarsch, H., Kokkinis, I. (2018). The Expected Duration of Sequential Gossiping. In: Belardinelli, F., Argente, E. (eds) Multi-Agent Systems and Agreement Technologies. EUMAS AT 2017 2017. Lecture Notes in Computer Science(), vol 10767. Springer, Cham. https://doi.org/10.1007/978-3-030-01713-2_10

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  • DOI: https://doi.org/10.1007/978-3-030-01713-2_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-01712-5

  • Online ISBN: 978-3-030-01713-2

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