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Synchronous Rendezvous for Location-Aware Agents

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Part of the book series:Lecture Notes in Computer Science ((LNTCS,volume 6950))

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Abstract

We study rendezvous of two anonymous agents, where each agent knows its own initial position in the environment. Their task is to meet each other as quickly as possible. The time of the rendezvous is measured by the number of synchronous rounds that agents need to use in the worst case in order to meet. In each round, an agent may make a simple move or it may stay motionless. We consider two types of environments, finite or infinite graphs and Euclidean spaces. A simple move traverses a single edge (in a graph) or at most a unit distance (in Euclidean space). The rendezvous consists in visiting by both agents the same point of the environment simultaneously (in the same round).

In this paper, we propose several asymptotically optimal rendezvous algorithms. In particular, we show that in the line and trees as well as in multi-dimensional Euclidean spaces and grids the agents can rendezvous in time\(\mathcal{O}(d)\), whered is the distance between the initial positions of the agents.

The problem of location-aware rendezvous was studied before in the asynchronous model for Euclidean spaces and multi-dimensional grids, where the emphasis was on the length of the adopted rendezvous trajectory. We point out that, contrary to the asynchronous case, where the cost of rendezvous is dominated by the size of potentially large neighborhoods, the agents are able to meet in all graphs of at mostn nodes in time almost linear ind, namely,\(\mathcal{O}(d \log^2 n)\). We also determine an infinite family of graphs in which synchronized rendezvous takes time Ω(d).

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Author information

Authors and Affiliations

  1. University of Liverpool, Liverpool, L69 3BX, UK

    Andrew Collins, Leszek Gąsieniec & Russell Martin

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

    Jurek Czyzowicz

  3. INRIA Bordeaux Sud-Ouest, LaBRI, 33405, Talence, France

    Adrian Kosowski

Authors
  1. Andrew Collins

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  2. Jurek Czyzowicz

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  3. Leszek Gąsieniec

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  4. Adrian Kosowski

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  5. Russell Martin

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Editor information

Editors and Affiliations

  1. Department of Computer Science, Weizmann Institute of Science, Rehovot, Israel

    David Peleg

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© 2011 Springer-Verlag Berlin Heidelberg

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Collins, A., Czyzowicz, J., Gąsieniec, L., Kosowski, A., Martin, R. (2011). Synchronous Rendezvous for Location-Aware Agents. In: Peleg, D. (eds) Distributed Computing. DISC 2011. Lecture Notes in Computer Science, vol 6950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24100-0_42

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