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Deterministic Rendezvous of Asynchronous Bounded-Memory Agents in Polygonal Terrains

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Abstract

Two mobile agents, modeled as points starting at different locations of an unknown terrain, have to meet. The terrain is a polygon with polygonal holes. We consider two versions of this rendezvous problem: exact RV, when the points representing the agents have to coincide at some time, and ε-RV, when these points have to get at distance less than ε in the terrain. In any terrain, each agent chooses its trajectory, but the movements of the agent on this trajectory are controlled by an adversary that may, e.g., speed up or slow down the agent. Agents have bounded memory: their computational power is that of finite state machines. Our aim is to compare the feasibility of exact and of ε-RV when agents are anonymous vs. when they are labeled. We show classes of polygonal terrains which distinguish all the studied scenarios from the point of view of feasibility of rendezvous. The features which influence the feasibility of rendezvous include symmetries present in the terrains, boundedness of their diameter, and the number of vertices of polygons in the terrains.

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Notes

  1. Notice that our definition of the walk allows the adversary not only to speed up or slow down the agent but also to 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. In fact our impossibility results hold even for an adversary that can only speed up or slow down the agent, without moving it back.

  2. Reorienting the agent’s compass is implemented by adding a fixed correction to its reading.

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Acknowledgements

Research of J. Czyzowicz was partially supported by NSERC discovery grant. Work of A. Kosowski was done during this author’s visit at the Université du Québec en Outaouais and was partially supported by Polish Ministry Grant N206 491738. Research of A. Pelc was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais.

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Authors and Affiliations

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

    Jurek Czyzowicz & Andrzej Pelc

  2. INRIA Bordeaux Sud-Ouest, CEPAGE Project, 33400, Talence, France

    Adrian Kosowski

  3. Department of Algorithms and System Modeling, Gdańsk University of Technology, 80233, Gdańsk, Poland

    Adrian Kosowski

Authors
  1. Jurek Czyzowicz
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  2. Adrian Kosowski
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  3. Andrzej Pelc
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Correspondence to Adrian Kosowski.

Additional information

A preliminary version of this paper appeared in the Proc. 35th International Symposiums on Mathematical Foundations of Computer Science (MFCS 2010), LNCS 6281.

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Czyzowicz, J., Kosowski, A. & Pelc, A. Deterministic Rendezvous of Asynchronous Bounded-Memory Agents in Polygonal Terrains. Theory Comput Syst 52, 179–199 (2013). https://doi.org/10.1007/s00224-011-9379-7

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