Skip to main content
SpringerLink
Log in

Stationary and Deterministic Leader Election in Self-organizing Particle Systems

  • Conference paper
  • First Online:
Stabilization, Safety, and Security of Distributed Systems (SSS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11914))

Abstract

We propose the first stationary and deterministic protocol for the leader election problem for non-simply connected particle systems in the geometric Amoebot model in which particles have no unique identifiers but have common chirality. The solution does not require particle movement to break symmetry (stationary) and does not allow particles to make probabilistic choices (deterministic). We show that leader election is possible if and only if the proposed protocol succeeds in electing a unique leader. We show that if the protocol fails to elect a leader, it will always succeed in finding a finite set of \(k \le 6\) leader candidates and the system must have k-symmetry that prevents the selection of less than k candidates. The protocols runs in \(O(n^2)\) steps, where n is the number of particles in the system. Other solutions to the leader election problem in the Amoebot model are either probabilistic, assume that the system is simply connected, and/or require stronger primitives to break symmetry.

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

Notes

  1. 1.

    We should note here that the concept of a border node is a logical construct introduced by this paper and is different from particles.

References

  1. Abu-Amara, H.H.: Fault-tolerant distributed algorithms for agreement and election. Ph.D. thesis, University of Illinois, Champaign, IL, USA (1988)

    Google Scholar 

  2. Afek, Y., Brown, G.M.: Self-stabilization of the alternating-bit protocol. In: SRDS 1989, pp. 80–83. IEEE (1989)

    Google Scholar 

  3. Cannon, S., Daymude, J.J., Randall, D., Richa, A.W.: A Markov chain algorithm for compression in self-organizing particle systems. In: PODC, pp. 279–288. ACM (2016)

    Google Scholar 

  4. Daymude, J.J., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Improved leader election for self-organizing programmable matter. In: Fernández Anta, A., Jurdzinski, T., Mosteiro, M.A., Zhang, Y. (eds.) ALGOSENSORS 2017. LNCS, vol. 10718, pp. 127–140. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-72751-6_10

    Chapter  Google Scholar 

  5. Derakhshandeh, Z., Dolev, S., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Brief announcement: amoebot–a new model for programmable matter. In: SPAA, pp. 220–222. ACM (2014)

    Google Scholar 

  6. Derakhshandeh, Z., Gmyr, R., Porter, A., Richa, A.W., Scheideler, C., Strothmann, T.: On the runtime of universal coating for programmable matter. In: Rondelez, Y., Woods, D. (eds.) DNA 2016. LNCS, vol. 9818, pp. 148–164. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-43994-5_10

    Chapter  Google Scholar 

  7. Derakhshandeh, Z., Gmyr, R., Richa, A.W., Scheideler, C., Strothmann, T.: Universal coating for programmable matter. Theoret. Comput. Sci. 671, 56–68 (2017)

    Article  MathSciNet  Google Scholar 

  8. Derakhshandeh, Z., Gmyr, R., Strothmann, T., Bazzi, R.A., Richa, A.W., Scheideler, C.: Leader election and shape formation with self-organizing programmable matter. Comput. Mol. Program. DNA 21, 117–132 (2015)

    Article  MathSciNet  Google Scholar 

  9. Emek, Y., Kutten, S., Lavi, R., Moses Jr., W.K.: Deterministic leader election in programmable matter. In: ICALP, 9–12 July, pp. 140:1–140:14 (2019)

    Google Scholar 

  10. Flocchini, P., Prencipe, G., Santoro, N.: Distributed computing by oblivious mobile robots. Synth. Lect. Distrib. Comput. Theory 3(2), 1–185 (2012)

    Article  Google Scholar 

  11. Flocchini, P., Prencipe, G., Santoro, N., Widmayer, P.: Arbitrary pattern formation by asynchronous, anonymous, oblivious robots. Theoret. Comput. Sci. 407(1–3), 412–447 (2008)

    Article  MathSciNet  Google Scholar 

  12. Gastineau, N., Abdou, W., Mbarek, N., Togni, O.: Distributed leader election and computation of local identifiers for programmable matter. In: Gilbert, S., Hughes, D., Krishnamachari, B. (eds.) ALGOSENSORS 2018. LNCS, vol. 11410, pp. 159–179. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-14094-6_11

    Chapter  Google Scholar 

  13. Ghaffari, M., Haeupler, B.: Near optimal leader election in multi-hop radio networks. In: SODA, pp. 748–766 (2013)

    Google Scholar 

  14. Itai, A., Rodeh, M.: Symmetry breaking in distributed networks. Inf. Comput. 88(1), 60–87 (1990)

    Article  MathSciNet  Google Scholar 

  15. Karpov, V., Karpova, I.: Leader election algorithms for static swarms. Biol. Inspired Cogn. Archit. 12, 54–64 (2015)

    Google Scholar 

  16. Luna, G.A.D., Flocchini, P., Santoro, N., Viglietta, G., Yamauchi, Y.: Shape formation by programmable particles. In: 21st International Conference on Principles of Distributed Systems, OPODIS 2017, pp. 31:1–31:16 (2017)

    Google Scholar 

  17. Lynch, N.A.: Distributed Algorithms. Elsevier, Amsterdam (1996)

    MATH  Google Scholar 

  18. Peleg, D.: Time-optimal leader election in general networks. J. Parallel Distrib. Comput. 8(1), 96–99 (1990)

    Article  Google Scholar 

  19. Styer, E.F.: Symmetry Breaking on networks of processes. Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA, USA (1989)

    Google Scholar 

Download references

Acknowledgements

We would like to thank Shay Kutten for helpful discussions about the topic of this paper and for suggesting the example with two particles that we used in the conclusion section.

Author information

Authors and Affiliations

  1. Arizona State University, Tempe, AZ, USA

    Rida A. Bazzi & Joseph L. Briones

Authors
  1. Rida A. Bazzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joseph L. Briones
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rida A. Bazzi .

Editor information

Editors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Mohsen Ghaffari

  2. Kent State University, Kent, OH, USA

    Mikhail Nesterenko

  3. Sorbonne University, Paris, France

    Sébastien Tixeuil

  4. CEA LIST, Gif-sur-Yvette, France

    Sara Tucci

  5. Kyushu University, Fukuoka, Japan

    Yukiko Yamauchi

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bazzi, R.A., Briones, J.L. (2019). Stationary and Deterministic Leader Election in Self-organizing Particle Systems. In: Ghaffari, M., Nesterenko, M., Tixeuil, S., Tucci, S., Yamauchi, Y. (eds) Stabilization, Safety, and Security of Distributed Systems. SSS 2019. Lecture Notes in Computer Science(), vol 11914. Springer, Cham. https://doi.org/10.1007/978-3-030-34992-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-34992-9_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34991-2

  • Online ISBN: 978-3-030-34992-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation