Logarithmic Expected-Time Leader Election in Population Protocol Model

  • Yuichi SudoEmail author
  • Fukuhito Ooshita
  • Taisuke Izumi
  • Hirotsugu Kakugawa
  • Toshimitsu Masuzawa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11914)


In this paper, we present the first leader election protocol in the population protocol model that stabilizes within \(O(\log n)\) parallel time in expectation with \(O(\log n)\) states per agent, where n is the number of agents. Given a rough knowledge m of the population size n such that \(m \ge \log _2 n\) and \(m=O(\log n)\), the proposed protocol guarantees that exactly one leader is elected and the unique leader is kept forever thereafter.


  1. 1.
    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)zbMATHGoogle Scholar
  2. 2.
    Alistarh, D., Gelashvili, R.: Polylogarithmic-time leader election in population protocols. In: Halldórsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 479–491. Springer, Heidelberg (2015). Scholar
  3. 3.
    Alistarh, D., Aspnes, J., Eisenstat, D., Gelashvili, R., Rivest, R.L.: Time-space trade-offs in population protocols. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2560–2579. SIAM (2017)Google Scholar
  4. 4.
    Alistarh, D., Aspnes, J., Gelashvili, R.: Space-optimal majority in population protocols. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2221–2239. SIAM (2018)Google Scholar
  5. 5.
    Gąsieniec, L., Staehowiak, G.: Fast space optimal leader election in population protocols. In: Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 2653–2667. SIAM (2018)Google Scholar
  6. 6.
    Gąsieniec, L., Stachowiak, G., Uznański, P.: Almost logarithmic-time space optimal leader election in population protocols. arXiv preprint arXiv: 1802.06867 (2018)
  7. 7.
    Michail, O., Spirakis, P.G., Theofilatos, M.: Simple and fast approximate counting and leader election in populations. In: Izumi, T., Kuznetsov, P. (eds.) SSS 2018. LNCS, vol. 11201, pp. 154–169. Springer, Cham (2018). Scholar
  8. 8.
    Doty, D., Soloveichik, D.: Stable leader election in population protocols requires linear time. Distrib. Comput. 31(4), 257–271 (2018)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Sudo, Y., Masuzawa, T.: Leader election requires logarithmic time in population protocols. arXiv preprint arXiv:1906.11121 (2019)
  10. 10.
    Sudo, Y., Nakamura, J., Yamauchi, Y., Ooshita, F., Kakugawa, H., Masuzawa, T.: Loosely-stabilizing leader election in a population protocol model. Theor. Comput. Sci. 444, 100–112 (2012) MathSciNetCrossRefGoogle Scholar
  11. 11.
    Sudo, Y., Ooshita, F., Kakugawa, H., Masuzawa, T., Datta, A.K., Larmore, L.L.: Loosely-stabilizing leader election with polylogarithmic convergence time. In: 22nd International Conference on Principles of Distributed Systems, OPODIS 2018, pp. 30:1–30:16 (2018)Google Scholar
  12. 12.
    Bilke, A., Cooper, C., Elsässer, R., Radzik, T.: Brief announcement: population protocols for leader election and exact majority with \(o(log^2 n)\) states and \(o(log^2 n)\) convergence time. In: Proceedings of the 38th ACM Symposium on Principles of Distributed Computing, pp. 451–453. Springer (2017)Google Scholar
  13. 13.
    Alistarh, D., Gelashvili, R.: Recent algorithmic advances in population protocols. ACM SIGACT News 49(3), 63–73 (2018)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Elsässer, R., Radzik, T.: Recent results in population protocols for exact majority and leaderelection. Bull. EATCS 3(126), 1–34 (2018)Google Scholar
  15. 15.
    Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. Distrib. Comput. 21(3), 183–199 (2008)CrossRefGoogle Scholar
  16. 16.
    Sudo, Y., Ooshita, F., Izumi, T., Kakugawa, H., Masuzawa, T.: Logarithmic expected-time leader election in population protocol model. arXiv preprint arXiv:1812.11309 (2018)

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Yuichi Sudo
    • 1
    Email author
  • Fukuhito Ooshita
    • 2
  • Taisuke Izumi
    • 3
  • Hirotsugu Kakugawa
    • 4
  • Toshimitsu Masuzawa
    • 1
  1. 1.Osaka UniversitySuitaJapan
  2. 2.Nara Institute of Science and TechnologyIkomaJapan
  3. 3.Nagoya Institute of TechnologyNagoyaJapan
  4. 4.Ryukoku UniversityOtsuJapan

Personalised recommendations