Advertisement

Rendezvous of Mobile Agents without Agreement on Local Orientation

  • Jérémie Chalopin
  • Shantanu Das
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6199)

Abstract

The exploration of a connected graph by multiple mobile agents has been previously studied under different conditions. A fundamental coordination problem in this context is the gathering of all agents at a single node, called the Rendezvous problem. To allow deterministic exploration, it is usually assumed that the edges incident to a node are locally ordered according to a fixed function called local orientation. We show that having a fixed local orientation is not necessary for solving rendezvous; Two or more agents having possibly distinct local orientation functions can rendezvous in all instances where rendezvous is solvable under a common local orientation function. This result is surprising and extends the known characterization of solvable instances for rendezvous and leader election in anonymous networks. On one hand, our model is more general than the anonymous port-to-port network model and on the other hand it is less powerful than qualitative model of Barrière et al. [4,9] where the agents have distinct labels. Our results hold even in the simplest model of communication using identical tokens and in fact, we show that using two tokens per agent is necessary and sufficient for solving the problem.

Keywords

Distributed Coordination Mobile Agents Rendezvous Synchronization Anonymous Networks Incomparable Labels 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer, Dordrecht (2003)zbMATHGoogle Scholar
  2. 2.
    Angluin, D.: Local and global properties in networks of processors. In: Proc. 12th Symposium on Theory of Computing (STOC 1980), pp. 82–93 (1980)Google Scholar
  3. 3.
    Boldi, P., Codenotti, B., Gemmell, P., Shammah, S., Simon, J., Vigna, S.: Symmetry breaking in anonymous networks: characterizations. In: Proc. 4th Israeli Symp. on Theory of Computing and Systems (ISTCS 1996), pp. 16–26 (1996)Google Scholar
  4. 4.
    Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Can we elect if we cannot compare? In: Proc. 15th Symp. on Parallel Algorithms and Architectures (SPAA), pp. 324–332 (2003)Google Scholar
  5. 5.
    Baston, V., Gal, S.: Rendezvous search when marks are left at the starting points. Naval Research Logistics 48(8), 722–731 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Boldi, P., Vigna, S.: Fibrations of graphs. Discrete Mathematics 243(1-3), 21–66 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chalopin, J., Godard, E., Métivier, Y., Ossamy, R.: Mobile agent algorithms versus message passing algorithms. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 187–201. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Chalopin, J., Godard, E., Métivier, Y., Tel, G.: About the termination detection in the asynchronous message passing model. In: van Leeuwen, J., Italiano, G.F., van der Hoek, W., Meinel, C., Sack, H., Plášil, F. (eds.) SOFSEM 2007. LNCS, vol. 4362, pp. 200–211. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Chalopin, J.: Election and rendezvous with incomparable labels. Theoretical Computer Science 399(1-2), 54–70 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Czyzowicz, J., Labourel, A., Pelc, A.: How to meet asynchronously (almost) everywhere. In: Proc. ACM Symp. on Discrete Algorithms (SODA 2010), pp. 22–30 (2010)Google Scholar
  11. 11.
    Das, S., Flocchini, P., Nayak, A., Kutten, S., Santoro, N.: Map Construction of Unknown Graphs by Multiple Agents. Theoretical Computer Science 385(1-3), 34–48 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Das, S., Flocchini, P., Nayak, A., Santoro, N.: Effective elections for anonymous mobile agents. In: Asano, T. (ed.) ISAAC 2006. LNCS, vol. 4288, pp. 732–743. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Fraigniaud, P., Pelc, A.: Deterministic rendezvous in trees with little memory. In: Taubenfeld, G. (ed.) DISC 2008. LNCS, vol. 5218, pp. 242–256. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    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
  15. 15.
    Lovász, L., Plummer, M.D.: Matching Theory. Annals of Discrete Mathematics, vol. 29. North-Holland, Amsterdam (1986)zbMATHGoogle Scholar
  16. 16.
    Yamashita, M., Kameda, T.: Computing on anonymous networks: Part I - characterizing the solvable cases. IEEE Transactions on Parallel and Distributed Systems 7(1), 69–89 (1996)CrossRefGoogle Scholar
  17. 17.
    Yamashita, M., Kameda, T.: Leader election problem on networks in which processor identity numbers are not distinct. IEEE Transactions on Parallel and Distributed Systems 10(9), 878–887 (1999)CrossRefGoogle Scholar
  18. 18.
    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 2010

Authors and Affiliations

  • Jérémie Chalopin
    • 1
  • Shantanu Das
    • 1
  1. 1.LIF, CNRS & Aix Marseille UniversitéMarseille cedex 13France

Personalised recommendations