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Optimal Probabilistic Ring Exploration by Semi-synchronous Oblivious Robots

  • Stéphane Devismes
  • Franck Petit
  • Sébastien Tixeuil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5869)

Abstract

We consider a team of k identical, oblivious, semi-synchronous mobile robots that are able to sense (i.e., view) their environment, yet are unable to communicate, and evolve on a constrained path. Previous results in this weak scenario show that initial symmetry yields high lower bounds when problems are to be solved by deterministic robots.

In this paper, we initiate research on probabilistic bounds and solutions in this context, and focus on the exploration problem of anonymous unoriented rings of any size. It is known that Θ(logn) robots are necessary and sufficient to solve the problem with k deterministic robots, provided that k and n are coprime. By contrast, we show that four identical probabilistic robots are necessary and sufficient to solve the same problem, also removing the coprime constraint. Our positive results are constructive.

Keywords

Mobile Robot Visibility Sensor Robot Move Sequential Computation Limited Visibility 
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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References

  1. 1.
    Asahiro, Y., Fujita, S., Suzuki, I., Yamashita, M.: A self-stabilizing marching algorithm for a group of oblivious robots. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 125–144. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Souissi, S., Défago, X., Yamashita, M.: Using eventually consistent compasses to gather memory-less mobile robots with limited visibility. TAAS 4(1) (2009)Google Scholar
  3. 3.
    Suzuki, I., Yamashita, M.: Distributed anonymous mobile robots: Formation of geometric patterns. SIAM J. Comput. 28(4), 1347–1363 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theor. Comput. Sci. 407(1-3), 412–447 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Dieudonné, Y., Labbani-Igbida, O., Petit, F.: Circle formation of weak mobile robots. TAAS 3(4) (2008)Google Scholar
  6. 6.
    Dieudonné, Y., Petit, F.: Scatter of weak mobile robots. Parallel Processing Letters 19(1), 175–184 (2009)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ando, H., Oasa, Y., Suzuki, I., Yamashita, M.: Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Transactions on Robotics and Automation (1999)Google Scholar
  8. 8.
    Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Gathering of asynchronous robots with limited visibility. Theor. Comput. Sci. 337(1-3), 147–168 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Bouzid, Z., Potop-Butucaru, M.G., Tixeuil, S.: Byzantine-resilient convergence in oblivious robot networks. In: Garg, V., Wattenhofer, R., Kothapalli, K. (eds.) ICDCN 2009. LNCS, vol. 5408, Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Klasing, R., Markou, E., Pelc, A.: Gathering asynchronous oblivious mobile robots in a ring. Theor. Comput. Sci. 390(1), 27–39 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Klasing, R., Kosowski, A., Navarra, A.: Taking advantage of symmetries: Gathering of asynchronous oblivious robots on a ring. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 446–462. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    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
  13. 13.
    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
  14. 14.
    Efrima, A., Peleg, D.: Distributed algorithms for partitioning a swarm of autonomous mobile robots. Theor. Comput. Sci. 410(14), 1355–1368 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Devismes, S., Petit, F., Tixeuil, S.: Optimal probabilistic ring exploration by asynchronous oblivious robots. Technical Report inria-00360305, INRIA (February 2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stéphane Devismes
    • 1
  • Franck Petit
    • 2
  • Sébastien Tixeuil
    • 3
  1. 1.VERIMAG UMR 5104Université Joseph FourierGrenobleFrance
  2. 2.INRIA, LIP UMR 5668Université de Lyon / ENS LyonFrance
  3. 3.INRIA Grand LargeUniversité Pierre et Marie CurieParis 6France

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