Optimal Deterministic Ring Exploration with Oblivious Asynchronous Robots

  • Anissa Lamani
  • Maria Gradinariu Potop-Butucaru
  • Sébastien Tixeuil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6058)


We consider the problem of exploring an anonymous unoriented ring of size n by k identical, oblivious, asynchronous mobile robots, that are unable to communicate, yet have the ability to sense their environment and take decisions based on their local view. Previous works in this weak scenario prove that k must not divide n for a deterministic solution to exist. Also, it is known that the minimum number of robots (either deterministic or probabilistic) to explore a ring of size n is 4. An upper bound of 17 robots holds in the deterministic case while 4 probabilistic robots are sufficient. In this paper, we close the complexity gap in the deterministic setting, by proving that no deterministic exploration is feasible with less than five robots, and that five robots are sufficient for any n that is coprime with five. Our protocol completes exploration in O(n) robot moves, which is also optimal.


Robots Anonymity Obliviousness Exploration Asynch-ronous system Ring 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Das, S., Flocchini, P., Kutten, S., Nayak, A., Santoro, N.: Map construction of unknown graphs by multiple agents. Theoretical Computer Science 385, 34–48 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    De Marco, G., Gargano, L., Kranakis, E., Krizanc, D., Pelc, A., Vaccaro, U.: Asynchronous deterministic rendezvous in graphs. Theoretical Computer Science 355, 315–326 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Devismes, S., Petit, F., Tixeuil, S.: Optimal probabilistic ring exploration by asynchronous oblivious robots. In: Proceedings of SIROCCO 2009 (2009)Google Scholar
  4. 4.
    Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. TAAS 3(16) (2008)Google Scholar
  5. 5.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Computing without communicating: Ring exploration by asynchronous oblivious robots. In: Tovar, E., Tsigas, P., Fouchal, H. (eds.) OPODIS 2007. LNCS, vol. 4878, pp. 105–118. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Flocchini, P., Ilcinkas, D., Pelc, A., Santoro, N.: Remembering without memory: Tree exploration by asynchronous oblivious robots. In: Shvartsman, A.A., Felber, P. (eds.) SIROCCO 2008. LNCS, vol. 5058, pp. 33–47. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Flocchini, P., Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Multiple mobile agent rendezvous in a ring. In: Farach-Colton, M. (ed.) LATIN 2004. LNCS, vol. 2976, pp. 599–608. Springer, Heidelberg (2004)Google Scholar
  8. 8.
    Flocchini, P., Prencipe, P., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theoretical Computer Science 407, 412–447 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: Gathering of asynchronous oblivious robots on a ring. In: OPODIS, pp. 446–462 (2008)Google Scholar
  10. 10.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theoretical Computer Science 390, 27–39 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kowalski, D., Pelc, A.: Polynomial deterministic rendezvous in arbitrary graphs. In: Fleischer, R., Trippen, G. (eds.) ISAAC 2004. LNCS, vol. 3341, pp. 644–656. Springer, Heidelberg (2004)Google Scholar
  12. 12.
    Lamani, A., Potop-Butucaru, M., Tixeuil, S.: Optimal deterministic ring exploration with oblivious asynchronous robots. CoRR abs/0910.0832 (2009)Google Scholar
  13. 13.
    Prencipe, G.: CORDA: Distributed coordination of a set of autonomous mobile robots. In: Proc. 4th European Research Seminar on Advances in Distributed Systems (ERSADS 2001), Bertinoro, Italy, May 2001, pp. 185–190 (2001)Google Scholar
  14. 14.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM Journal on Computing 28(4), 1347–1363 (1999)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Anissa Lamani
    • 1
  • Maria Gradinariu Potop-Butucaru
    • 1
  • Sébastien Tixeuil
    • 1
  1. 1.LIP6-CNRSUniversité Pierre et Marie Curie - Paris 6France

Personalised recommendations