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Asynchronous Rendezvous of Anonymous Agents in Arbitrary Graphs

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Principles of Distributed Systems (OPODIS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7109))

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Abstract

Two identical (anonymous) mobile agents have to meet in an arbitrary, possibly infinite, unknown connected graph. Agents are modeled as points, they start at nodes of the graph chosen by the adversary and the route of each of them only depends on the already traversed portion of the graph and, in the case of randomized rendezvous, on the result of coin tossing. The actual walk of each agent also depends on an asynchronous adversary that may arbitrarily vary the speed of the agent, stop it, or even move it back and forth, as long as the walk of the agent in each segment of its route is continuous, does not leave it and covers all of it. Meeting means that both agents must be at the same time in some node or in some point inside an edge of the graph.

In the deterministic scenario we characterize the initial positions of the agents for which rendezvous is feasible and we provide an algorithm guaranteeing asynchronous rendezvous from all such positions in an arbitrary connected graph. In the randomized scenario we show an algorithm that achieves asynchronous rendezvous with probability 1, for arbitrary initial positions in an arbitrary connected graph. In both cases the graph may be finite or (countably) infinite.

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Authors and Affiliations

  1. Département d’informatique, Université du Québec en Outaouais, Gatineau, Québec, J8X 3X7, Canada

    Samuel Guilbault & Andrzej Pelc

Authors
  1. Samuel Guilbault
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  2. Andrzej Pelc
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Editor information

Editors and Affiliations

  1. Institute IMDEA Networks, Avenida del Mar Mediterraneo, 22, 28918, Leganes, Madrid, Spain

    Antonio Fernàndez Anta

  2. CEIICP, RETIS Lab, Scuola Superiore Sant’Anna, Via Moruzzi 1, 56127, Pisa, Italy

    Giuseppe Lipari

  3. Dependability Group (TSF), LAAS-CNRS, 7 av du colonel Roche, 31077, Toulouse, France

    Matthieu Roy

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Guilbault, S., Pelc, A. (2011). Asynchronous Rendezvous of Anonymous Agents in Arbitrary Graphs. In: Fernàndez Anta, A., Lipari, G., Roy, M. (eds) Principles of Distributed Systems. OPODIS 2011. Lecture Notes in Computer Science, vol 7109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25873-2_29

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  • DOI: https://doi.org/10.1007/978-3-642-25873-2_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25872-5

  • Online ISBN: 978-3-642-25873-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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