Skip to main content
SpringerLink
Log in

The Power of Global Knowledge on Self-stabilizing Population Protocols

  • Conference paper
  • First Online:
Structural Information and Communication Complexity (SIROCCO 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12156))

Abstract

In the population protocol model, many problems cannot be solved in a self-stabilizing way. However, global knowledge, such as the number of nodes in a network, sometimes allow us to design a self-stabilizing protocol for such problems. In this paper, we investigate the effect of global knowledge on the possibility of self-stabilizing population protocols in arbitrary graphs. Specifically, we clarify the solvability of the leader election problem, the ranking problem, the degree recognition problem, and the neighbor recognition problem by self-stabilizing population protocols with knowledge of the number of nodes and/or the number of edges in a network.

This work was supported by JSPS KAKENHI Grant Numbers 17K19977, 18K18000, 18K18029, 18K18031, 19H04085, and 20H04140 and JST SICORP Grant Number JPMJSC1606.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    In [4], D is defined as the diameter of the graph, not a known upper bound on it. However, since we must take into account an arbitrary initial configuration, we require an upper bound on the diameter; Otherwise, the agents need the memory of unbounded size. Fortunately, the knowledge of the upper bound is not a strong assumption in this case: any upper bound which is polynomial in the true diameter is acceptable since the space complexity is \(O(\log D)\) bits.

References

  1. 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). https://doi.org/10.1007/978-3-662-47666-6_38

    Chapter  Google Scholar 

  2. 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)

    Article  Google Scholar 

  3. Angluin, D., Aspnes, J., Eisenstat, D.: Fast computation by population protocols with a leader. Distrib. Comput. 21(3), 183–199 (2008)

    Article  Google Scholar 

  4. Angluin, D., Aspnes, J., Fischer, M.J., Jiang, H.: Self-stabilizing population protocols. ACM Trans. Auton. Adapt. Syst. 3(4), 13 (2008)

    Article  Google Scholar 

  5. Beauquier, J., Blanchard, P., Burman, J.: Self-stabilizing leader election in population protocols over arbitrary communication graphs. In: Baldoni, R., Nisse, N., van Steen, M. (eds.) OPODIS 2013. LNCS, vol. 8304, pp. 38–52. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-03850-6_4

    Chapter  Google Scholar 

  6. Burman, J., Doty, D., Nowak, T., Severson, E.E., Xu, C.: Efficient self-stabilizing leader election in population protocols. arXiv preprint arXiv:1907.06068 (2019)

  7. 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. Theory Comput. Syst. 50(3), 433–445 (2012)

    Article  MathSciNet  Google Scholar 

  8. Canepa, D., Potop-Butucaru, M.G.: Stabilizing leader election in population protocols (2007). http://hal.inria.fr/inria-00166632

  9. Chen, H.-P., Chen, H.-L.: Self-stabilizing leader election. In: Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, pp. 53–59 (2019)

    Google Scholar 

  10. Cordasco, G., Gargano, L.: Space-optimal proportion consensus with population protocols. In: Spirakis, P., Tsigas, P. (eds.) SSS 2017. LNCS, vol. 10616, pp. 384–398. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69084-1_28

    Chapter  Google Scholar 

  11. Dijkstra, E.: Self-stabilizing systems in spite of distributed control. Commun. ACM 17(11), 643–644 (1974)

    Article  Google Scholar 

  12. 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). https://doi.org/10.1007/11945529_28

    Chapter  Google Scholar 

  13. Gąsieniec, L., Stachowiak, G., Uznanski, P.: Almost logarithmic-time space optimal leader election in population protocols. In: The 31st ACM on Symposium on Parallelism in Algorithms and Architectures, pp. 93–102. ACM (2019)

    Google Scholar 

  14. Izumi, T.: On space and time complexity of loosely-stabilizing leader election. In: Scheideler, C. (ed.) SIROCCO 2014. LNCS, vol. 9439, pp. 299–312. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25258-2_21

    Chapter  MATH  Google Scholar 

  15. Mertzios, G.B., Nikoletseas, S.E., Raptopoulos, C.L., Spirakis, P.G.: Determining majority in networks with local interactions and very small local memory. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014. LNCS, vol. 8572, pp. 871–882. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43948-7_72

    Chapter  MATH  Google Scholar 

  16. Sudo, Y., Masuzawa, T., Datta, A.K., Larmore, L.L.: The same speed timer in population protocols. In: The 36th IEEE International Conference on Distributed Computing Systems, pp. 252–261 (2016)

    Google Scholar 

  17. 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)

    Article  MathSciNet  Google Scholar 

  18. Sudo, Y., Ooshita, F., Izumi, T., Kakugawa, H., Masuzawa, T.: Logarithmic expected-time leader election in population protocol model. In: Ghaffari, M., Nesterenko, M., Tixeuil, S., Tucci, S., Yamauchi, Y. (eds.) SSS 2019. LNCS, vol. 11914, pp. 323–337. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34992-9_26

    Chapter  Google Scholar 

  19. Sudo, Y., Ooshita, F., Kakugawa, H., Masuzawa, T.: Loosely-stabilizing leader election on arbitrary graphs in population protocols. In: Aguilera, M.K., Querzoni, L., Shapiro, M. (eds.) OPODIS 2014. LNCS, vol. 8878, pp. 339–354. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-14472-6_23

    Chapter  Google Scholar 

  20. Sudo, Y., Ooshita, F., Kakugawa, H., Masuzawa, T.: Loosely stabilizing leader election on arbitrary graphs in population protocols without identifiers or random numbers. IEICE Trans. Inf. Syst. 103(3), 489–499 (2020)

    Article  Google Scholar 

  21. Sudo, Y., Ooshita, F., Kakugawa, H., Masuzawa, T., Datta, A.K., Larmore, L.L.: Loosely-stabilizing leader election with polylogarithmic convergence time. Theor. Comput. Sci. 806, 617–631 (2020)

    Article  MathSciNet  Google Scholar 

  22. Sudo, Y., Shibata, M., Nakamura, J., Kim, Y., Masuzawa, T.: The power of global knowledge on self-stabilizing population protocols. arXiv preprint arXiv:2003.07491 (2020)

Download references

Author information

Authors and Affiliations

  1. Osaka University, Osaka, Japan

    Yuichi Sudo & Toshimitsu Masuzawa

  2. Kyushu Institute of Technology, Fukuoka, Japan

    Masahiro Shibata

  3. Toyohashi University of Technology, Aichi, Japan

    Junya Nakamura

  4. Nagoya Institute of Technology, Aichi, Japan

    Yonghwan Kim

Authors
  1. Yuichi Sudo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masahiro Shibata
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Junya Nakamura
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yonghwan Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Toshimitsu Masuzawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuichi Sudo .

Editor information

Editors and Affiliations

  1. Computer Science, CIDSE, Arizona State University, Tempe, AZ, USA

    Andrea Werneck Richa

  2. Department of Computer Science, Paderborn University, Paderborn, Germany

    Christian Scheideler

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Sudo, Y., Shibata, M., Nakamura, J., Kim, Y., Masuzawa, T. (2020). The Power of Global Knowledge on Self-stabilizing Population Protocols. In: Richa, A., Scheideler, C. (eds) Structural Information and Communication Complexity. SIROCCO 2020. Lecture Notes in Computer Science(), vol 12156. Springer, Cham. https://doi.org/10.1007/978-3-030-54921-3_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-54921-3_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-54920-6

  • Online ISBN: 978-3-030-54921-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation