Document Open Access Logo

Deterministic Self-Stabilising Leader Election for Programmable Matter with Constant Memory

Authors Jérémie Chalopin , Shantanu Das , Maria Kokkou

PDF
Thumbnail PDF

File

LIPIcs.DISC.2024.13.pdf
  • Filesize: 0.79 MB
  • 17 pages

Document Identifiers

Author Details

Jérémie Chalopin
  • Aix Marseille Univ, CNRS, LIS, Marseille, France
Shantanu Das
  • Aix Marseille Univ, CNRS, LIS, Marseille, France
Maria Kokkou
  • Aix Marseille Univ, CNRS, LIS, Marseille, France

Funding

This work has been partially supported by ANR project DUCAT (ANR-20-CE48-0006).

Cite As Get BibTex

Jérémie Chalopin, Shantanu Das, and Maria Kokkou. Deterministic Self-Stabilising Leader Election for Programmable Matter with Constant Memory. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 13:1-13:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.DISC.2024.13

Abstract

The problem of electing a unique leader is central to all distributed systems, including programmable matter systems where particles have constant size memory. In this paper, we present a silent self-stabilising, deterministic, stationary, election algorithm for particles having constant memory, assuming that the system is simply connected. Our algorithm is elegant and simple, and requires constant memory per particle. We prove that our algorithm always stabilises to a configuration with a unique leader, under a daemon satisfying some fairness guarantees (Gouda fairness [Mohamed G. Gouda, 2001]). We use the special geometric properties of programmable matter in 2D triangular grids to obtain the first self-stabilising algorithm for such systems. This result is surprising since it is known that silent self-stabilising algorithms for election in general distributed networks require Ω(log n) bits of memory per node, even for ring topologies [Shlomi Dolev et al., 1999].

Subject Classification

ACM Subject Classification
  • Computer systems organization → Fault-tolerant network topologies
  • Computing methodologies → Self-organization
Keywords
  • Leader Election
  • Programmable Matter
  • Self-Stabilisation
  • Silent
  • Deterministic
  • Unique Leader
  • Simply Connected
  • Gouda fair Daemon
  • Constant Memory

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Dana Angluin, James Aspnes, David Eisenstat, and Eric Ruppert. The computational power of population protocols. Distributed Comput., 20(4):279-304, 2007. URL: https://doi.org/10.1007/s00446-007-0040-2.
  2. Baruch Awerbuch and Rafail Ostrovsky. Memory-efficient and self-stabilizing network reset. In PODC 1994, pages 254-263. ACM, 1994. URL: https://doi.org/10.1145/197917.198104.
  3. Rida A. Bazzi and Joseph L. Briones. Stationary and deterministic leader election in self-organizing particle systems. In SSS 2019, volume 11914 of Lecture Notes in Comput. Sci., pages 22-37. Springer, 2019. URL: https://doi.org/10.1007/978-3-030-34992-9_3.
  4. Lélia Blin, Laurent Feuilloley, and Gabriel Le Bouder. Optimal space lower bound for deterministic self-stabilizing leader election algorithms. Discret. Math. Theor. Comput. Sci., 25, 2023. URL: https://doi.org/10.46298/dmtcs.9335.
  5. Lélia Blin, Pierre Fraigniaud, and Boaz Patt-Shamir. On proof-labeling schemes versus silent self-stabilizing algorithms. In SSS 2014, volume 8756 of Lecture Notes in Comput. Sci., pages 18-32. Springer, 2014. URL: https://doi.org/10.1007/978-3-319-11764-5_2.
  6. Lélia Blin and Sébastien Tixeuil. Compact deterministic self-stabilizing leader election on a ring: the exponential advantage of being talkative. Distributed Comput., 31(2):139-166, 2018. URL: https://doi.org/10.1007/s00446-017-0294-2.
  7. Paolo Boldi and Sebastiano Vigna. Universal dynamic synchronous self-stabilization. Distributed Comput., 15:137-153, 2002. URL: https://doi.org/10.1007/s004460100062.
  8. Joseph L. Briones, Tishya Chhabra, Joshua J. Daymude, and Andréa W. Richa. Invited paper: Asynchronous deterministic leader election in three-dimensional programmable matter. In ICDCN 2023, pages 38-47. ACM, 2023. URL: https://doi.org/10.1145/3571306.3571389.
  9. Shukai Cai, Taisuke Izumi, and Koichi Wada. 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. URL: https://doi.org/10.1007/s00224-011-9313-z.
  10. Jérémie Chalopin, Shantanu Das, and Maria Kokkou. Deterministic leader election for stationary programmable matter with common direction. In SIROCCO 2024, volume 14662 of Lecture Notes in Comput. Sci., pages 174-191. Springer, 2024. URL: https://doi.org/10.1007/978-3-031-60603-8_10.
  11. Jérémie Chalopin, Shantanu Das, and Maria Kokkou. Deterministic self-stabilising leader election for programmable matter with constant memory. arXiv preprint, 2024. URL: https://doi.org/10.48550/arXiv.2408.08775.
  12. Ajoy Kumar Datta, Lawrence L. Larmore, and Priyanka Vemula. Self-stabilizing leader election in optimal space under an arbitrary scheduler. Theor. Comput. Sci., 412(40):5541-5561, 2011. URL: https://doi.org/10.1016/j.tcs.2010.05.001.
  13. Joshua J. Daymude, Andréa W. Richa, and Christian Scheideler. The canonical Amoebot model: Algorithms and concurrency control. Distributed Comput., 36(2):159-192, 2023. URL: https://doi.org/10.1007/s00446-023-00443-3.
  14. Joshua J. Daymude, Andréa W. Richa, and Jamison W. Weber. Bio-inspired energy distribution for programmable matter. In ICDCN 2021, pages 86-95. ACM, 2021. URL: https://doi.org/10.1145/3427796.3427835.
  15. Zahra Derakhshandeh, Shlomi Dolev, Robert Gmyr, Andréa W Richa, Christian Scheideler, and Thim Strothmann. Amoebot - A new model for programmable matter. In SPAA 2014, pages 220-222. ACM, 2014. URL: https://doi.org/10.1145/2612669.2612712.
  16. Zahra Derakhshandeh, Robert Gmyr, Thim Strothmann, Rida A. Bazzi, Andréa W. Richa, and Christian Scheideler. Leader election and shape formation with self-organizing programmable matter. In DNA 2015, volume 9211 of Lecture Notes in Comput. Sci., pages 117-132. Springer, 2015. URL: https://doi.org/10.1007/978-3-319-21999-8_8.
  17. Giuseppe Antonio Di Luna, Paola Flocchini, Nicola Santoro, Giovanni Viglietta, and Yukiko Yamauchi. Shape formation by programmable particles. Distributed Comput., 33(1):69-101, 2020. URL: https://doi.org/10.1007/s00446-019-00350-6.
  18. Edsger W. Dijkstra. Self-stabilizing systems in spite of distributed control. Commun. ACM, 17(11):643-644, 1974. URL: https://doi.org/10.1145/361179.361202.
  19. Shlomi Dolev. Self-Stabilization. MIT Press, 2000. URL: https://doi.org/10.7551/mitpress/6156.001.0001.
  20. Shlomi Dolev, Mohamed G. Gouda, and Marco Schneider. Memory requirements for silent stabilization. Acta Inf., 36(6):447-462, 1999. URL: https://doi.org/10.1007/s002360050180.
  21. Swan Dubois and Sébastien Tixeuil. A taxonomy of daemons in self-stabilization. arXiv preprint, 2011. URL: https://doi.org/10.48550/arXiv.1110.0334.
  22. Fabien Dufoulon, Shay Kutten, and William K. Moses Jr. Efficient deterministic leader election for programmable matter. In PODC 2021, pages 103-113. ACM, 2021. URL: https://doi.org/10.1145/3465084.3467900.
  23. Yuval Emek, Shay Kutten, Ron Lavi, and William K Moses Jr. Deterministic leader election in programmable matter. In ICALP 2019, volume 132 of LIPIcs Leibniz Int. Proc. Inform., pages 140:1-140:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. URL: https://doi.org/10.4230/LIPIcs.ICALP.2019.140.
  24. Sándor P. Fekete, Robert Gmyr, Sabrina Hugo, Phillip Keldenich, Christian Scheffer, and Arne Schmidt. Cadbots: Algorithmic aspects of manipulating programmable matter with finite automata. Algorithmica, 83(1):387-412, 2021. URL: https://doi.org/10.1007/s00453-020-00761-z.
  25. Nicolas Gastineau, Wahabou Abdou, Nader Mbarek, and Olivier Togni. Distributed leader election and computation of local identifiers for programmable matter. In ALGOSENSORS 2018, volume 11410 of Lecture Notes in Comput. Sci., pages 159-179. Springer, 2018. URL: https://doi.org/10.1007/978-3-030-14094-6_11.
  26. Nicolas Gastineau, Wahabou Abdou, Nader Mbarek, and Olivier Togni. Leader election and local identifiers for three-dimensional programmable matter. Concurr. Comput. Pract. Exp., 34(7), 2022. URL: https://doi.org/10.1002/cpe.6067.
  27. Mohamed G. Gouda. The theory of weak stabilization. In WSS 2001, volume 2194 of Lecture Notes in Comput. Sci., pages 114-123. Springer, 2001. URL: https://doi.org/10.1007/3-540-45438-1_8.
  28. Elliot Hawkes, Byoungkwon An, Nadia M. Benbernou, H. Tanaka, Sangbae Kim, Erik D. Demaine, Daniela Rus, and Robert J. Wood. Programmable matter by folding. Proc. Natl. Acad. Sci., 107(28):12441-12445, 2010. URL: https://doi.org/10.1073/pnas.0914069107.
  29. Gene Itkis and Leonid Levin. Fast and lean self-stabilizing asynchronous protocols. In FOCS 1994, pages 226-239. IEEE Computer Society, 1994. URL: https://doi.org/10.1109/SFCS.1994.365691.
  30. Gene Itkis, Chengdian Lin, and Janos Simon. Deterministic, constant space, self-stabilizing leader election on uniform rings. In WDAG 1995, volume 972 of Lecture Notes in Comput. Sci., pages 288-302. Springer, 1995. URL: https://doi.org/10.1007/BFb0022154.
  31. Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. Distributed Comput., 22(4):215-233, 2010. URL: https://doi.org/10.1007/s00446-010-0095-3.
  32. Gérard Le Lann. Distributed systems - towards a formal approach. In IFIP 1977, pages 155-160. North-Holland, 1977. URL: https://inria.hal.science/hal-03504338.
  33. Tommaso Toffoli and Norman Margolus. Programmable matter: Concepts and realization. Int. J. High Speed Comput., 5(2):155-170, 1993. URL: https://doi.org/10.1016/0167-2789(91)90296-L.
  34. John von Neumann. Theory of Self-Reproducing Automata. University of Illinois Press, 1966. URL: https://dl.acm.org/doi/book/10.5555/1102024.
  35. Damien Woods, Ho-Lin Chen, Scott Goodfriend, Nadine Dabby, Erik Winfree, and Peng Yin. Active self-assembly of algorithmic shapes and patterns in polylogarithmic time. In ITCS 2013, pages 353-354. ACM, 2013. URL: https://doi.org/10.1145/2422436.2422476.
  36. Masafumi Yamashita and Tiko Kameda. Computing on an anonymous network. In PODC 1988, pages 117-130. ACM, 1988. URL: https://doi.org/10.1145/62546.62568.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact