How to Gather Asynchronous Oblivious Robots on Anonymous Rings

  • Gianlorenzo D’Angelo
  • Gabriele Di Stefano
  • Alfredo Navarra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7611)


A set of robots arbitrarily placed on different nodes of an anonymous ring have to meet at one common node and remain in there. This problem is known in the literature as the gathering. Anonymous and oblivious robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), decides whether to stay idle or to move to one of its neighbors (Compute), and in the latter case makes the computed move instantaneously (Move). Cycles are asynchronous among robots. Moreover, each robot is empowered by the so called multiplicity detection capability, that is, it is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one.

The described problem has been extensively studied during the last years. However, the known solutions work only for specific initial configurations and leave some open cases. In this paper, we provide an algorithm which solves the general problem, and is able to detect all the ungatherable configurations. It is worth noting that our new algorithm makes use of a unified and general strategy for any initial configuration, even those left open by previous works.


Mobile Robot Common Node Single Robot Axis Passing Mobile Entity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Alpern, S.: The rendezvous search problem. SIAM J. Control Optim. 33, 673–683 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bampas, E., Czyzowicz, J., Gąsieniec, L., Ilcinkas, D., Labourel, A.: Almost Optimal Asynchronous Rendezvous in Infinite Multidimensional Grids. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 297–311. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Blin, L., Milani, A., Potop-Butucaru, M., Tixeuil, S.: Exclusive Perpetual Ring Exploration without Chirality. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 312–327. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Chalopin, J., Das, S.: Rendezvous of Mobile Agents without Agreement on Local Orientation. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 515–526. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Cord-Landwehr, A., Degener, B., Fischer, M., Hüllmann, M., Kempkes, B., Klaas, A., Kling, P., Kurras, S., Märtens, M., Meyer auf der Heide, F., Raupach, C., Swierkot, K., Warner, D., Weddemann, C., Wonisch, D.: A New Approach for Analyzing Convergence Algorithms for Mobile Robots. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 650–661. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  6. 6.
    Czyzowicz, J., Labourel, A., Pelc, A.: How to meet asynchronously (almost) everywhere. In: Proc. of the 21st ACM-SIAM Symp. on Discrete Algorithms (SODA), pp. 22–30 (2010)Google Scholar
  7. 7.
    D’Angelo, G., Di Stefano, G., Klasing, R., Navarra, A.: Gathering of Robots on Anonymous Grids without Multiplicity Detection. In: Even, G., Halldórsson, M.M. (eds.) SIROCCO 2012. LNCS, vol. 7355, pp. 327–338. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    D’Angelo, G., Di Stefano, G., Navarra, A.: Gathering of Six Robots on Anonymous Symmetric Rings. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 174–185. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    D’Angelo, G., Di Stefano, G., Navarra, A.: How to gather asynchronous oblivious robots on anonymous rings. Rapport de recherche RR-7963, INRIA (2012)Google Scholar
  10. 10.
    Degener, B., Kempkes, B., Langner, T., Meyer, F.: auf der Heide, P. Pietrzyk, and R. Wattenhofer. A tight runtime bound for synchronous gathering of autonomous robots with limited visibility. In: Proc. of the 23rd ACM Symp. on Parallelism in Algorithms and Architectures (SPAA), pp. 139–148 (2011)Google Scholar
  11. 11.
    Dessmark, A., Fraigniaud, P., Kowalski, D., Pelc, A.: Deterministic rendezvous in graphs. Algorithmica 46, 69–96 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Computing without communicating: Ring exploration by asynchronous oblivious robots. Algorithmica (to appear)Google Scholar
  13. 13.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Remembering without memory: Tree exploration by asynchronous oblivious robots. Theoretical Computer Science 411(14-15), 1583–1598 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci. 337, 147–168 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Randomized Gathering of Mobile Robots with Local-Multiplicity Detection. In: Guerraoui, R., Petit, F. (eds.) SSS 2009. LNCS, vol. 5873, pp. 384–398. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Izumi, T., Izumi, T., Kamei, S., Ooshita, F.: Mobile Robots Gathering Algorithm with Local Weak Multiplicity in Rings. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 101–113. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  17. 17.
    Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Asynchronous Mobile Robot Gathering from Symmetric Configurations without Global Multiplicity Detection. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 150–161. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Kamei, S., Lamani, A., Ooshita, F., Tixeuil, S.: Asynchronous mobile robot gathering from symmetric configurations without global multiplicity detection. In: Proceedings of the 37th International Symposium on Mathematical Foundations of Computer Science (MFCS). Springer (to appear, 2012)Google Scholar
  19. 19.
    Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: Gathering of many asynchronous oblivious robots on a ring. Theor. Comput. Sci. 411, 3235–3246 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 20.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390, 27–39 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 21.
    Koren, M.: Gathering small number of mobile asynchronous robots on ring. Zeszyty Naukowe Wydzialu ETI Politechniki Gdanskiej. Technologie Informacyjne 18, 325–331 (2010)Google Scholar
  22. 22.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Yamashita, M., Souissi, S., Défago, X.: Gathering two stateless mobile robots using very inaccurate compasses in finite time. In: Proc. of the 1st int. Conf. on Robot Communication and Coordination (RoboComm), pp. 48:1–48:4 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gianlorenzo D’Angelo
    • 1
  • Gabriele Di Stefano
    • 2
  • Alfredo Navarra
    • 3
  2. 2.Dipartimento di Ingegneria e Sceinze dell’Informazione e MatematicaUniversità degli Studi dell’AquilaItaly
  3. 3.Dipartimento di Matematica e InformaticaUniversità degli Studi di PerugiaItaly

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