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Randomized Rendezvous of Mobile Agents in Anonymous Unidirectional Ring Networks

  • Shinji Kawai
  • Fukuhito Ooshita
  • Hirotsugu Kakugawa
  • Toshimitsu Masuzawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7355)

Abstract

We consider the rendezvous problem of multiple (mobile) agents in anonymous unidirectional ring networks under the constraint that each agent knows neither the number of nodes nor the number of agents. First, we prove for any (small) constant p(0 < p ≤ 1) that there exists no randomized algorithm that solves, with probability p, the rendezvous problem with (terminal) detection. For this reason, we consider the relaxed rendezvous problem, called the rendezvous problem without detection that does not require termination detection. We prove that there exists no randomized algorithm that solves, with probability 1, the rendezvous problem without detection. For the remaining cases, we show the possibility, that is, we propose a randomized algorithm that solves, with any given constant probability p(0 < p < 1), the rendezvous problem without detection.

Keywords

Mobile Agent Single Node Correct Number Identical Node Impossibility Result 
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.
    Alpern, S., Baston, V.J., Essegaier, S.: Rendezvous search on a graph. Journal of Applied Probability 36(1), 223–231 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Baba, D., Izumi, T., Ooshita, F., Kakugawa, H., Masuzawa, T.: Space-Optimal Rendezvous of Mobile Agents in Asynchronous Trees. In: Patt-Shamir, B., Ekim, T. (eds.) SIROCCO 2010. LNCS, vol. 6058, pp. 86–100. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Barriere, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Rendezvous and election of mobile agents: impact of sense of direction. Theory of Computing Systems 40(2), 143–162 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Chalopin, J., Das, S., Widmayer, P.: Rendezvous of Mobile Agents in Directed Graphs. In: Lynch, N.A., Shvartsman, A.A. (eds.) DISC 2010. LNCS, vol. 6343, pp. 282–296. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Das, S., Mihalák, M., Šrámek, R., Vicari, E., Widmayer, P.: Rendezvous of Mobile Agents When Tokens Fail Anytime. In: Baker, T.P., Bui, A., Tixeuil, S. (eds.) OPODIS 2008. LNCS, vol. 5401, pp. 463–480. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  6. 6.
    Dieudonné, Y., Pelc, A.: Deterministic gathering of anonymous agents in arbitrary networks. Arxiv preprint arXiv:1111.0321 (2011)Google Scholar
  7. 7.
    Gasieniec, L., Pelc, A., Radzik, T., Zhang, X.: Tree exploration with logarithmic memory. In: Proc. of SODA, pp. 585–594 (2007)Google Scholar
  8. 8.
    Kranakis, E., Krizanc, D.: An Algorithmic Theory of Mobile Agents. In: Montanari, U., Sannella, D., Bruni, R. (eds.) TGC 2006. LNCS, vol. 4661, pp. 86–97. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Kranakis, E., Krizanc, D., Markou, E.: Mobile Agent Rendezvous in a Synchronous Torus. In: Correa, J.R., Hevia, A., Kiwi, M. (eds.) LATIN 2006. LNCS, vol. 3887, pp. 653–664. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Kranakis, E., Krizanc, D., Markou, E.: The mobile agent rendezvous problem in the ring. Synthesis Lectures on Distributed Computing Theory, Lecture # 1. Morgan & Claypool Publishers (2010)Google Scholar
  11. 11.
    Kranakis, E., Krizanc, D., Morin, P.: Randomized Rendez-Vous with Limited Memory. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008. LNCS, vol. 4957, pp. 605–616. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Sudo, Y., Baba, D., Nakamura, J., Ooshita, F., Kakugawa, H., Masuzawa, T.: An agent exploration in unknown undirected graphs with whiteboards. In: Proc. of WRAS, p. 8 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Shinji Kawai
    • 1
  • Fukuhito Ooshita
    • 1
  • Hirotsugu Kakugawa
    • 1
  • Toshimitsu Masuzawa
    • 1
  1. 1.Graduate School of Information Science and TechnologyOsaka UniversityJapan

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