Theory of Computing Systems

, Volume 52, Issue 2, pp 179–199 | Cite as

Deterministic Rendezvous of Asynchronous Bounded-Memory Agents in Polygonal Terrains



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.


Mobile agent Rendezvous Deterministic Polygon Obstacle Bounded memory 



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.


  1. 1.
    Alpern, S.: The rendezvous search problem. SIAM J. Control Optim. 33, 673–683 (1995) MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Int. Series in Operations Research and Management Science, vol. 55. Kluwer Academic, Norwell (2002) Google Scholar
  3. 3.
    Alpern, J., Baston, V., Essegaier, S.: Rendezvous search on a graph. J. Appl. Probab. 36, 223–231 (1999) MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Anderson, E., Fekete, S.: Two-dimensional rendezvous search. Oper. Res. 49, 107–118 (2001) MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Baston, V., Gal, S.: Rendezvous on the line when the players’ initial distance is given by an unknown probability distribution. SIAM J. Control Optim. 36, 1880–1889 (1998) MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bilo, D., Disser, Y., Mihalak, M., Suri, S., Vicari, E., Widmayer, P.: Reconstructing visibility graphs with simple robots. In: Proc. 16th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2009). LNCS, vol. 5869, pp. 87–99 (2009) Google Scholar
  7. 7.
    Cieliebak, M., Flocchini, P., Prencipe, G., Santoro, N.: Solving the robots gathering problem. In: Proc. 30th International Colloquium on Automata, Languages and Programming (ICALP 2003). LNCS, vol. 2719, pp. 1181–1196 (2003) CrossRefGoogle Scholar
  8. 8.
    Czyzowicz, J., Ilcinkas, D., Labourel, A., Pelc, A.: Asynchronous deterministic rendezvous in bounded terrains. In: Proc. 17th International Colloquium on Structural Information and Communication Complexity (SIROCCO 2010). LNCS, vol. 6058, pp. 72–85 (2010) Google Scholar
  9. 9.
    Czyzowicz, J., Labourel, A., Pelc, A.: How to meet asynchronously (almost) everywhere. In: Proc. 21st Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2010), pp. 22–30 (2010) Google Scholar
  10. 10.
    De Marco, G., Gargano, L., Kranakis, E., Krizanc, D., Pelc, A., Vaccaro, U.: Asynchronous deterministic rendezvous in graphs. Theor. Comput. Sci. 355, 315–326 (2006) CrossRefMATHGoogle Scholar
  11. 11.
    Dessmark, A., Fraigniaud, P., Kowalski, D., Pelc, A.: Deterministic rendezvous in graphs. Algorithmica 46, 69–96 (2006) MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous oblivious robots with limited visibility. In: Proc. 18th Annual Symposium on Theoretical Aspects of Computer Science (STACS 2001). LNCS, vol. 2010, pp. 247–258 (2001) Google Scholar
  13. 13.
    Fraigniaud, P., Pelc, A.: Deterministic rendezvous in trees with little memory. In: Proc. 22nd International Symposium on Distributed Computing (DISC 2008). LNCS, vol. 5218, pp. 242–256 (2008) Google Scholar
  14. 14.
    Gal, S.: Rendezvous search on the line. Oper. Res. 47, 974–976 (1999) CrossRefMATHGoogle Scholar
  15. 15.
    Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: gathering of asynchronous oblivious robots on a ring. In: Proc. 12th International Conference on Principles of Distributed Systems (OPODIS 2008). LNCS, vol. 5401, pp. 446–462 (2008) Google Scholar
  16. 16.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390, 27–39 (2008) MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Kowalski, D., Malinowski, A.: How to meet in anonymous network. Theor. Comput. Sci. 399, 141–156 (2008) MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Mobile agent rendezvous in a ring. In: Proc. 23rd International Conference on Distributed Computing Systems (ICDCS 2003), pp. 592–599 (2003) CrossRefGoogle Scholar
  19. 19.
    Prencipe, G.: Impossibility of gathering by a set of autonomous mobile robots. Theor. Comput. Sci. 384, 222–231 (2007) MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Stachowiak, G.: Asynchronous Deterministic Rendezvous on the Line. In: Proc. 35th Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM 2009). LNCS, vol. 5404, pp. 497–508 (2009) Google Scholar
  21. 21.
    Ta-Shma, A., Zwick, U.: Deterministic rendezvous, treasure hunts and strongly universal exploration sequences. In: Proc. 18th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), pp. 599–608 (2007) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Jurek Czyzowicz
    • 1
  • Adrian Kosowski
    • 2
    • 3
  • Andrzej Pelc
    • 1
  1. 1.Département d’informatiqueUniversité du Québec en OutaouaisGatineauCanada
  2. 2.INRIA Bordeaux Sud-OuestCEPAGE ProjectTalenceFrance
  3. 3.Department of Algorithms and System ModelingGdańsk University of TechnologyGdańskPoland

Personalised recommendations