Optimal Memory Rendezvous of Anonymous Mobile Agents in a Unidirectional Ring

  • L. Gąsieniec
  • E. Kranakis
  • D. Krizanc
  • X. Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3831)


We study the rendezvous problem with k≥2 mobile agents in a n-node ring. We present a new algorithm which solves the rendezvous problem for any non-periodic distribution of agents on the ring. The mobile agents require the use of O(log k)–bit-wise size of internal memory and one indistinguishable token each. In the periodic (but not symmetric) case our new procedure allows the agents to conclude that rendezvous is not feasible. It is known that in the symmetric case the agents cannot decide the feasibility of rendezvous if their internal memory is limited to ω(loglog n) bits, see [15]. In this context we show new space optimal deterministic algorithm allowing effective recognition of the symmetric case. The algorithm is based on O(log k + loglog n)-bit internal memory and a single token provided to each mobile agent. Finally, it is known that both in the periodic as well as in the symmetric cases the rendezvous cannot be accomplished by any deterministic procedure due to problems with breaking symmetry.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alpern, S.: Asymmetric Rendezvous on the Circle. Dynamics and Control 10, 33–45 (2000)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alpern, S.: Rendezvous Search: A Personal Perspective. LSE Research Report, CDAM-2000-05, London School of Economics (2000)Google Scholar
  3. 3.
    Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer Academic Publishers, Dordrecht (2003)MATHGoogle Scholar
  4. 4.
    Alpern, S., Howard, J.V.: Alternating Search at Two Locations. LSE OR Working Paper, 99.30 (1999)Google Scholar
  5. 5.
    Alpern, S., Reyniers, D.: The Rendezvous and Coordinated Search Problems. Proceedings of the 33rd Conference on Decision and Control, Lake Buena Vista, FL (December 1994)Google Scholar
  6. 6.
    Anderson, E.J., Essegaier, S.: Rendezvous Search on the Line with Indistinguishable Players. SIAM J. of Control and Opt. 33, 1637–1642 (1995)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Anderson, E.J., Fekete, S.: Two-Dimensional Rendezvous Search. Operations Research 49, 107–188 (2001)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Anderson, E.J., Weber, R.R.: The Rendezvous Problem on Discrete Locations. Journal of Applied Probability 28, 839–851 (1990)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Apostol, T.M.: Introduction to Analytical Number Theory. Springer, Heidelberg (1997)Google Scholar
  10. 10.
    Baston, V., Gal, S.: Rendezvous on the Line When the Players’ Initial Distance is Given by an Unknown Probability Distribution. SIAM Journal of Control and Optimization 36(6), 1880–1889 (1998)MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Baston, V., Gal, S.: Rendezvous Search When Marks are Left at the Starting Points. Naval Research Logistics 47(6), 722–731 (2001)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Chester, E., Tutuncu, R.: Rendezvous Search on the Labeled Line, Old title: Rendezvous Search on Finite Domains, Preprint, Department of Mathematical Sciences, Carnegie Mellon University (2001)Google Scholar
  13. 13.
    Flocchini, P., Mans, B., Santoro, N.: Sense of Direction in Distributed Computing. Theoretical Computer Science 291(1), 29–53 (2003)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Flocchini, P., Kranakis, E., Krizanc, D., Santoro, N., Sawchuk, C.: The Rendezvous Search Problem with More Than Two Mobile Agents. Preprint (2002)Google Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    Frederickson, G.N., Lynch, N.A.: Electing a Leader in a Synchronous Ring. Journal of the ACM 1(34), 98–115 (1987)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Lim, W.S., Beck, A., Alpern, S.: Rendezvous Search on the Line with More Than Two Players. Operations Research 45, 357–364 (1997)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Pikounis, M., Thomas, L.C.: Many Player Rendezvous Search: Stick Together or Split and Meet? Working Paper 98/7, University of Edinburgh, Management School (1998)Google Scholar
  19. 19.
    Sawchuk, C.: Mobile Agent Rendezvous in the Ring. PhD Thesis, Carleton University (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • L. Gąsieniec
    • 1
  • E. Kranakis
    • 2
  • D. Krizanc
    • 3
  • X. Zhang
    • 1
  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK
  2. 2.School of Computer ScienceCarleton UniversityOttawaCanada
  3. 3.Computer Science Group, Mathematics DepartmentWesleyan UniversityMiddletownUSA

Personalised recommendations