The Power of Tokens: Rendezvous and Symmetry Detection for Two Mobile Agents in a Ring

  • Jurek Czyzowicz
  • Stefan Dobrev
  • Evangelos Kranakis
  • Danny Krizanc
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4910)

Abstract

Rendezvous with detection differs from the usual rendezvous problem in that two mobile agents not only accomplish rendezvous whenever this is possible, but can also detect the impossibility of rendezvous (e.g., due to symmetrical initial positions of the agents) in which case they are able to halt. We study the problem of rendezvous with and without detection of two anonymous mobile agents in a synchronous ring. The agents have constant memory and each of them possess one or more tokens which may be left at some nodes of the ring and noticed later. We derive sharp bounds for the case of at most two tokens per agent and also explore trade-offs between the number of tokens available to the agents and the time needed to accomplish rendezvous with detection.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alpern, S.: Rendezvous search: A personal perspective. Operations Research 50(5), 772–795 (2002)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer Academic Publishers, Norwell, Massachusetts (2003)MATHGoogle Scholar
  3. 3.
    Dobrev, S., Flocchini, P., Prencipe, G., Santoro, N.: Multiple agents rendezvous in a ring in spite of a black hole. In: Papatriantafilou, M., Hunel, P. (eds.) OPODIS 2003. LNCS, vol. 3144, pp. 34–46. Springer, Heidelberg (2004)Google Scholar
  4. 4.
    Knuth, D.: The Art of Computer Programming, Fundamental Algorithms, 3rd edn., vol. 1. Addison-Wesley, Reading (1997)Google Scholar
  5. 5.
    Kranakis, E., Krizanc, D.: An algorithmic theory of mobile agents. In: Roddick, J.F., Hornsby, K. (eds.)TGC 2006. LNCS, vol. 4661, Springer, Heidelberg (2007)Google Scholar
  6. 6.
    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, Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: Mobile agent rendezvous search problem in the ring. In: ICDCS. International Conference on Distributed Computing Systems, pp. 592–599 (2003)Google Scholar
  8. 8.
    Sawchuk, C.: Mobile Agent Rendezvous in the Ring. PhD thesis, Carleton University, School of Computer Science, Ottawa, Canada (2004)Google Scholar
  9. 9.
    Weiss, G.: Multiagent Systems: A Modern Approach to Distributed Artificial Intelligence. Wiley, Chichester (2002)Google Scholar
  10. 10.
    Yu, X., Yung, M.: Agent rendezvous: A dynamic symmetry-breaking problem. In: Meyer auf der Heide, F., Monien, B. (eds.) ICALP 1996. LNCS, vol. 1099, pp. 610–621. Springer, Heidelberg (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jurek Czyzowicz
    • 1
  • Stefan Dobrev
    • 2
  • Evangelos Kranakis
    • 3
  • Danny Krizanc
    • 4
  1. 1.Département d’informatique, Université du Québec en Outaouais, Gatineau, Québec J8X 3X7, Canada. Research supported in part by NSERC 
  2. 2.School of Information Technology and Engineering, University of Ottawa, Ottawa, Canada, on leave from Slovak Academy of Sciences, Bratislava, Slovakia., Research supported in part by NSERC 
  3. 3.School of Computer Science, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S 5B6, Canada. Research supported in part by NSERC and MITACS 
  4. 4.Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459USA

Personalised recommendations