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How to Meet in Anonymous Network

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Structural Information and Communication Complexity (SIROCCO 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4056))

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Abstract

A set of k mobile agents with distinct identifiers and located in nodes of an unknown anonymous connected network, have to meet at some node. We show that this gathering problem is no harder than its special case for k = 2, called the rendezvous problem, and design deterministic protocols solving the rendezvous problem with arbitrary startups in rings and in general networks. The measure of performance is the number of steps since the startup of the last agent until the rendezvous is achieved.

For rings we design an oblivious protocol with cost \({\cal O}(n\log \ell)\), where n is the size of the network and ℓ is the minimum label of participating agents. This result is asymptotically optimal due to the lower bound showed in [18].

For general networks we show a protocol with cost polynomial in n and logℓ, independent of the maximum difference τ of startup times, which answers in affirmative the open question from [22].

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Liverpool, Liverpool, L69 7ZF, UK

    Dariusz R. Kowalski

  2. Instytut Informatyki, Uniwersytet Warszawski, Banacha 2, 02-097, Warszawa, Poland

    Adam Malinowski

Authors
  1. Dariusz R. Kowalski
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  2. Adam Malinowski
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Editor information

Editors and Affiliations

  1. SITE, University of Ottawa, Canada

    Paola Flocchini

  2. Department of Computer Science, University of Liverpool, L69 3BX, Liverpool, UK

    Leszek Gąsieniec

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Kowalski, D.R., Malinowski, A. (2006). How to Meet in Anonymous Network. In: Flocchini, P., Gąsieniec, L. (eds) Structural Information and Communication Complexity. SIROCCO 2006. Lecture Notes in Computer Science, vol 4056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780823_5

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  • DOI: https://doi.org/10.1007/11780823_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35474-1

  • Online ISBN: 978-3-540-35475-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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