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Mediated Population Protocols: Leader Election and Applications

  • Shantanu Das
  • Giuseppe Antonio Di Luna
  • Paola Flocchini
  • Nicola Santoro
  • Giovanni Viglietta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)

Abstract

Mediated population protocols are an extension of population protocols in which communication links, as well as agents, have internal states. We study the leader election problem and some applications in constant-state mediated population protocols. Depending on the power of the adversarial scheduler, our algorithms are either stabilizing or allow the agents to explicitly reach a terminal state.

We show how to elect a unique leader if the graph of the possible interactions between agents is complete (as in the traditional population protocol model) or a tree. Moreover, we prove that a leader can be elected in a complete bipartite graph if and only if the two sides have coprime size.

We then describe how to take advantage of the presence of a leader to solve the tasks of token circulation and construction of a shortest-path spanning tree of the network. Finally, we prove that with a leader we can transform any stabilizing protocol into a terminating one that solves the same task.

References

  1. 1.
    Alistarh, D., Gelashvili, R., Vojnovic, M.: Fast and exact majority in population protocols. In: 34th Annual ACM Symposium on Principles of Distributed Computing, PODC, pp. 47–56 (2015)Google Scholar
  2. 2.
    Angluin, D., Aspnes, J., Chan, M., Fischer, M.J., Jiang, H., Peralta, R.: Stably computable properties of network graphs. In: Prasanna, V.K., Iyengar, S.S., Spirakis, P.G., Welsh, M. (eds.) DCOSS 2005. LNCS, vol. 3560, pp. 63–74. Springer, Heidelberg (2005). doi: 10.1007/11502593_8 CrossRefGoogle Scholar
  3. 3.
    Angluin, D., Aspnes, J., Diamadi, Z., Fischer, M.J., Peralta, R.: Computation in networks of passively mobile finite-state sensors. Distrib. Comput. 18(4), 235–253 (2006)CrossRefzbMATHGoogle Scholar
  4. 4.
    Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. ACM Trans. Auton. Adapt. Syst. 3(4), 1–28 (2008)CrossRefGoogle Scholar
  5. 5.
    Angluin, D., Aspnes, J., Eisenstat, D.: Stably computable predicates are semilinear. In: 25th Annual ACM Symposium on Principles of Distributed Computing, PODC, pp. 292–299 (2006)Google Scholar
  6. 6.
    Beauquier, J., Blanchard, P., Burman, J.: Self-stabilizing leader election in population protocols over arbitrary communication graphs. In: Baldoni, R., Nisse, N., Steen, M. (eds.) OPODIS 2013. LNCS, vol. 8304, pp. 38–52. Springer, Cham (2013). doi: 10.1007/978-3-319-03850-6_4 CrossRefGoogle Scholar
  7. 7.
    Beauquier, J., Burman, J., Clavière, S., Sohier, D.: Space-optimal counting in population protocols. In: Moses, Y. (ed.) DISC 2015. LNCS, vol. 9363, pp. 631–646. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48653-5_42 CrossRefGoogle Scholar
  8. 8.
    Beauquier, J., Burman, J., Kutten, S.: A self-stabilizing transformer for population protocols with covering. Theor. Comput. Sci. 412(33), 4247–4259 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Cai, S., Izumi, T., Wada, K.: How to prove impossibility under global fairness: on space complexity of self-stabilizing leader election on a population protocol model. Theor. Comput. Syst. 50(3), 433–445 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Canepa, D., Potop-Butucaru, M.G.: Stabilizing leader election in population protocols, Research Report, inria-00166632 (2007)Google Scholar
  11. 11.
    Canepa, D., Potop-Butucaru, M.G.: Self-stabilizing tiny interaction protocols. In: 3rd International Workshop on Reliability, Availability, and Security, WRAS, pp. 1–6 (2010)Google Scholar
  12. 12.
    Chatzigiannakis, I., Michail, O., Spirakis, P.G.: Stably decidable graph languages by mediated population protocols. In: Dolev, S., Cobb, J., Fischer, M., Yung, M. (eds.) SSS 2010. LNCS, vol. 6366, pp. 252–266. Springer, Heidelberg (2010). doi: 10.1007/978-3-642-16023-3_21 CrossRefGoogle Scholar
  13. 13.
    Chatzigiannakis, I., Michail, O., Spirakis, P.G.: Mediated population protocols. Theor. Comput. Sci. 412(22), 2434–2450 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Di Luna, G.A., Flocchini, P., Izumi, T., Izumi, T., Santoro, N., Viglietta, G.: Population protocols with faulty interactions: the impact of a leader. arXiv:1611.06864 [cs.DC] (2016)
  15. 15.
    Fischer, M., Jiang, H.: Self-stabilizing leader election in networks of finite-state anonymous agents. In: Shvartsman, M.M.A.A. (ed.) OPODIS 2006. LNCS, vol. 4305, pp. 395–409. Springer, Heidelberg (2006). doi: 10.1007/11945529_28 CrossRefGoogle Scholar
  16. 16.
    Mizoguchi, R., Hirotaka, O., Kijima, S., Yamashita, M.: On space complexity of self-stabilizing leader election in mediated population protocol. Distrib. Comput. 25(6), 451–460 (2012)CrossRefzbMATHGoogle Scholar
  17. 17.
    Shavit, N., Francez, N.: A new approach to detection of locally indicative stability. In: Kott, L. (ed.) ICALP 1986. LNCS, vol. 226, pp. 344–358. Springer, Heidelberg (1986). doi: 10.1007/3-540-16761-7_84 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Shantanu Das
    • 1
  • Giuseppe Antonio Di Luna
    • 2
  • Paola Flocchini
    • 2
  • Nicola Santoro
    • 3
  • Giovanni Viglietta
    • 2
  1. 1.LIF, Aix-Marseille University, and CNRSMarseilleFrance
  2. 2.University of OttawaOttawaCanada
  3. 3.Carleton UniversityOttawaCanada

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