Effective Elections for Anonymous Mobile Agents

  • Shantanu Das
  • Paola Flocchini
  • Amiya Nayak
  • Nicola Santoro
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4288)


We present distributed protocols for electing a leader among k mobile agents that are dispersed among the n nodes of a graph. While previous solutions for the agent election problem were restricted to specific topologies or under specific conditions, the protocols presented in this paper face the problem in the most general case, i.e. for an arbitrary topology where the nodes of the graph may not be distinctly labelled and the agents might be all identical (and thus indistinguishable from each other). In such cases, the agent election problem is often difficult, and sometimes impossible to solve using deterministic means. We have designed protocols for solving the problem that—unlike previous solutions—are effective, meaning that they always succeed in electing a leader under any given setting if at all it is possible, and otherwise detect the fact that election is impossible in that setting. We present several election protocols, all effective. Starting with the straightforward solution, that requires an exponential amount of edge-traversals by the agents, we describe significantly more efficient algorithms; in the latter the total number of edge-traversals made by the agents is always polynomial, their difference is in the amount of bits of storage they required at the nodes.


Mobile Agent Leader Election Span Forest Agent Move Election Algorithm 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alpern, S., Gal, S.: The Theory of Search Games and Rendezvous. Kluwer, Dordrecht (2003)MATHGoogle Scholar
  2. 2.
    Angluin, D.: Local and global properties in networks of processors. In: Proc. 12th ACM Symp. on Theory of Computing (STOC 1980), pp. 82–93 (1980)Google Scholar
  3. 3.
    Attiya, H., Snir, M., Warmuth, M.K.: Computing on an anonymous ring. Journal of ACM 35(4), 845–875 (1988)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Can we elect if we cannot compare? In: Proc. 15th ACM Symp. on Parallel Algorithms and Architectures (SPAA 2003), pp. 200–209 (2003)Google Scholar
  5. 5.
    Barrière, L., Flocchini, P., Fraigniaud, P., Santoro, N.: Election and rendezvous in fully anonymous networks with sense of direction. In: Theory of Computing Systems (to appear, 2006). Preliminary version in Proc. 10th Coll. on Structural Information and Communication Complexity (SIROCCO 2003), pp. 17–32 (2003) Google Scholar
  6. 6.
    Beame, P.W., Bodlaender, H.L.: Distributed computing on transitive grids: The torus. In: Cori, R., Monien, B. (eds.) STACS 1989. LNCS, vol. 349, pp. 294–303. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  7. 7.
    Bender, M., Fernandez, A., Ron, D., Sahai, A., Vadhan, S.: The power of a pebble: Exploring and mapping directed graphs. In: Proc. 30th ACM Symp. on Theory of Computing (STOC 1998), pp. 269–287 (1998)Google Scholar
  8. 8.
    Boldi, P., Shammah, S., Vigna, S., Codenotti, B., Gemmell, P., Simon, J.: Symmetry breaking in anonymous networks: Characterizations. In: Proc. 4th Israel Symp. on Theory of Computing and Systems, pp. 16–26 (1996)Google Scholar
  9. 9.
    Das, S., Flocchini, P., Kutten, S., Nayak, A., Santoro, N.: Map construction of unknown graphs by multiple agents. In: Pelc, A., Raynal, M. (eds.) SIROCCO 2005. LNCS, vol. 3499, pp. 99–114. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Fraigniaud, P., Ilcinkas, D.: Digraph exploration with little memory. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 246–257. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Gallager, R.G., Humblet, P.A., Spira, P.M.: A distributed algorithm for minimum-weight spanning trees. ACM Transactions on Programming Languages and Systems 5(1), 66–77 (1983)MATHCrossRefGoogle Scholar
  12. 12.
    Korach, E., Kutten, S., Moran, S.: A modular technique for the design of efficient distributed leader finding algorithms. ACM Transactions on Programming Languages and Systems 12(1), 84–101 (1990)CrossRefGoogle Scholar
  13. 13.
    Kranakis, E.: Symmetry and computability in anonymous networks: A brief survey. In: Proc. 3rd Int. Conf. on Structural Information and Communication Complexity (SIROCCO 1997), pp. 1–16 (1997)Google Scholar
  14. 14.
    Kranakis, E., Krizanc, D.: Distributed computing on anonymous hypercube networks. Journal of Algorithms 23(1), 32–50 (1997)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Norris, N.: Universal covers of graphs: Isomorphism to depth n − 1 implies isomorphism to all depths. Discrete Applied Mathematics 56(1), 61–74 (1995)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Sakamoto, N.: Comparison of initial conditions for distributed algorithms on anonymous networks. In: Proc. 18th ACM Symposium on Principles of Distributed Computing (PODC 1999), pp. 173–179 (1999)Google Scholar
  17. 17.
    Yamashita, M., Kameda, T.: Computing on anonymous networks: Parts I and II. IEEE Trans. on Parallel and Distributed Systems 7(1), 69–96 (1996)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Shantanu Das
    • 1
  • Paola Flocchini
    • 1
  • Amiya Nayak
    • 1
  • Nicola Santoro
    • 2
  1. 1.School of Information Technology and EngineeringUniversity of OttawaCanada
  2. 2.School of Computer ScienceCarleton UniversityCanada

Personalised recommendations