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Reachability and Expectation in Gossiping

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PRIMA 2017: Principles and Practice of Multi-Agent Systems (PRIMA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10621))

Abstract

We give combinatorial, computational and simulation results for well-known distributed protocols for gossiping on completely connected networks. The protocols consist of: making any call (\(\mathsf {ANY}\)), only calling agents whose secret you do not know (“learn new secrets” \(\mathsf {LNS}\)), and never repeating calls (“call once” \(\mathsf {CO}\)). First, we show that these protocols all differ in what distributions of secrets are reachable by their execution. Next, we formulate \(\mathsf {ANY}\) and \(\mathsf {LNS}\) as Markov chains. We present an algorithm that generates the states of these Markov chains and computes the exact value of the expected duration of the protocols. Finally, we study the asymptotic behaviour of \(\mathsf {LNS}\) via simulations, and compare this to the known result for \(\mathsf {ANY}\).

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Notes

  1. 1.

    This idea was presented to us by Dionysis Kakolyris.

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Acknowledgements

We are grateful to Christophe Chareton, George Giakkoupis, Dionysis Kakolyris, and Aris Pagourtzis for useful discussions and to the anonymous reviewers for many useful comments and suggestions. We acknowledge financial support from ERC project EPS 313360. Hans van Ditmarsch is also affiliated to IMSc, Chennai, as research associate.

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Authors and Affiliations

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

    Hans van Ditmarsch & Ioannis Kokkinis

  2. Technical University of Denmark, Kongens Lyngby, Denmark

    Anders Stockmarr

Authors
  1. Hans van Ditmarsch
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  2. Ioannis Kokkinis
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  3. Anders Stockmarr
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Corresponding author

Correspondence to Ioannis Kokkinis .

Editor information

Editors and Affiliations

  1. Nanyang Technological University, Singapore, Singapore

    Bo An

  2. Universidade Federal Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil

    Ana Bazzan

  3. Universidade Nova de Lisboa, Caparica, Portugal

    João Leite

  4. Université Côte d’Azur, Sophia Antipolis, France

    Serena Villata

  5. University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Leendert van der Torre

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van Ditmarsch, H., Kokkinis, I., Stockmarr, A. (2017). Reachability and Expectation in Gossiping. In: An, B., Bazzan, A., Leite, J., Villata, S., van der Torre, L. (eds) PRIMA 2017: Principles and Practice of Multi-Agent Systems. PRIMA 2017. Lecture Notes in Computer Science(), vol 10621. Springer, Cham. https://doi.org/10.1007/978-3-319-69131-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-69131-2_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-69130-5

  • Online ISBN: 978-3-319-69131-2

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