How to Meet in Anonymous Network

  • Dariusz R. Kowalski
  • Adam Malinowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4056)

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].

Keywords

mobile agents gathering rendezvous anonymous networks distributed algorithms 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Dariusz R. Kowalski
    • 1
  • Adam Malinowski
    • 2
  1. 1.Department of Computer ScienceThe University of LiverpoolLiverpoolUK
  2. 2.Instytut InformatykiUniwersytet WarszawskiWarszawaPoland

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