Document Open Access Logo

Uniform Bipartition in the Population Protocol Model with Arbitrary Communication Graphs

Authors Hiroto Yasumi, Fukuhito Ooshita, Michiko Inoue, Sébastien Tixeuil

PDF
Thumbnail PDF

File

LIPIcs.OPODIS.2020.33.pdf
  • Filesize: 499 kB
  • 16 pages

Document Identifiers

Author Details

Hiroto Yasumi
  • Nara Institute of Science and Technology, Japan
Fukuhito Ooshita
  • Nara Institute of Science and Technology, Japan
Michiko Inoue
  • Nara Institute of Science and Technology, Japan
Sébastien Tixeuil
  • Sorbonne Université, CNRS, LIP6, Paris, France

Funding

This work was supported by JSPS KAKENHI Grant Numbers 18K11167, 20H04140, 20J21849, and JST SICORP Grant Number JPMJSC1806. This work was partially funded by the ANR project SAPPORO, ref. 2019-CE25-0005-1.

Cite AsGet BibTex

Hiroto Yasumi, Fukuhito Ooshita, Michiko Inoue, and Sébastien Tixeuil. Uniform Bipartition in the Population Protocol Model with Arbitrary Communication Graphs. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 33:1-33:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.OPODIS.2020.33

Abstract

In this paper, we focus on the uniform bipartition problem in the population protocol model. This problem aims to divide a population into two groups of equal size. In particular, we consider the problem in the context of arbitrary communication graphs. As a result, we investigate the solvability of the uniform bipartition problem with arbitrary communication graphs when agents in the population have designated initial states, under various assumptions such as the existence of a base station, symmetry of the protocol, and fairness of the execution. When the problem is solvable, we present protocols for uniform bipartition. When global fairness is assumed, the space complexity of our solutions is tight.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Concurrent algorithms
Keywords
  • population protocol
  • uniform bipartition
  • distributed protocol

Metrics

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

Related Versions

References

  1. Dan Alistarh, James Aspnes, David Eisenstat, Rati Gelashvili, and Ronald L Rivest. Time-space trade-offs in population protocols. In Proc. of the 28th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2560-2579, 2017. Google Scholar
  2. Dan Alistarh, James Aspnes, and Rati Gelashvili. Space-optimal majority in population protocols. In Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 2221-2239. SIAM, 2018. Google Scholar
  3. Dan Alistarh and Rati Gelashvili. Polylogarithmic-time leader election in population protocols. In Proc. of the 42nd International Colloquium on Automata, Languages, and Programming, pages 479-491, 2015. Google Scholar
  4. Dana Angluin, James Aspnes, Melody Chan, Michael J Fischer, Hong Jiang, and René Peralta. Stably computable properties of network graphs. In Proc. of International Conference on Distributed Computing in Sensor Systems, pages 63-74, 2005. Google Scholar
  5. Dana Angluin, James Aspnes, Zoë Diamadi, Michael J Fischer, and René Peralta. Computation in networks of passively mobile finite-state sensors. Distributed computing, 18(4):235-253, 2006. Google Scholar
  6. Dana Angluin, James Aspnes, and David Eisenstat. A simple population protocol for fast robust approximate majority. Distributed Computing, 21(2):87-102, 2008. Google Scholar
  7. Dana Angluin, James Aspnes, Michael J Fischer, and Hong Jiang. Self-stabilizing population protocols. ACM Transactions on Autonomous and Adaptive Systems (TAAS), 3(4):13, 2008. Google Scholar
  8. James Aspnes, Joffroy Beauquier, Janna Burman, and Devan Sohier. Time and space optimal counting in population protocols. In Proc. of International Conference on Principles of Distributed Systems, pages 13:1-13:17, 2016. Google Scholar
  9. Joffroy Beauquier, Peva Blanchard, and Janna Burman. Self-stabilizing leader election in population protocols over arbitrary communication graphs. In International Conference on Principles of Distributed Systems, pages 38-52. Springer, 2013. Google Scholar
  10. Joffroy Beauquier, Janna Burman, Simon Claviere, and Devan Sohier. Space-optimal counting in population protocols. In Proc. of International Symposium on Distributed Computing, pages 631-646, 2015. Google Scholar
  11. Joffroy Beauquier, Julien Clement, Stephane Messika, Laurent Rosaz, and Brigitte Rozoy. Self-stabilizing counting in mobile sensor networks with a base station. In Proc. of International Symposium on Distributed Computing, pages 63-76, 2007. Google Scholar
  12. Stav Ben-Nun, Tsvi Kopelowitz, Matan Kraus, and Ely Porat. An o (log3/2 n) parallel time population protocol for majority with o (log n) states. In Proceedings of the 39th Symposium on Principles of Distributed Computing, pages 191-199, 2020. Google Scholar
  13. Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik. A population protocol for exact majority with o(log5/3 n) stabilization time and theta(log n) states. In 32nd International Symposium on Distributed Computing, DISC 2018, New Orleans, LA, USA, October 15-19, 2018, volume 121 of LIPIcs, pages 10:1-10:18, 2018. Google Scholar
  14. Petra Berenbrink, Robert Elsässer, Tom Friedetzky, Dominik Kaaser, Peter Kling, and Tomasz Radzik. Time-space trade-offs in population protocols for the majority problem. Distributed Computing, pages 1-21, 2020. Google Scholar
  15. Petra Berenbrink, George Giakkoupis, and Peter Kling. Optimal time and space leader election in population protocols. In Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing, pages 119-129, 2020. Google Scholar
  16. Petra Berenbrink, Dominik Kaaser, and Tomasz Radzik. On counting the population size. In Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing, pages 43-52, 2019. Google Scholar
  17. Olivier Bournez, Jérémie Chalopin, Johanne Cohen, Xavier Koegler, and Mikael Rabie. Population protocols that correspond to symmetric games. International Journal of Unconventional Computing, 9, 2013. Google Scholar
  18. Davide Canepa and Maria Gradinariu Potop-Butucaru. Self-stabilizing tiny interaction protocols. In Proceedings of the Third International Workshop on Reliability, Availability, and Security, page 10. ACM, 2010. Google Scholar
  19. Carole Delporte-Gallet, Hugues Fauconnier, Rachid Guerraoui, and Eric Ruppert. When birds die: Making population protocols fault-tolerant. Distributed Computing in Sensor Systems, pages 51-66, 2006. Google Scholar
  20. David Doty and David Soloveichik. Stable leader election in population protocols requires linear time. Distributed Computing, 31(4):257-271, 2018. Google Scholar
  21. Michael Fischer and Hong Jiang. Self-stabilizing leader election in networks of finite-state anonymous agents. In International Conference On Principles Of Distributed Systems, pages 395-409. Springer, 2006. Google Scholar
  22. Leszek Gąsieniec, David Hamilton, Russell Martin, Paul G Spirakis, and Grzegorz Stachowiak. Deterministic population protocols for exact majority and plurality. In Proc. of International Conference on Principles of Distributed Systems, pages 14:1-14:14, 2016. Google Scholar
  23. Leszek Gąsieniec, Grzegorz Stachowiak, and Przemyslaw Uznanski. Almost logarithmic-time space optimal leader election in population protocols. In The 31st ACM on Symposium on Parallelism in Algorithms and Architectures, pages 93-102. ACM, 2019. Google Scholar
  24. Tomoko Izumi, Keigo Kinpara, Taisuke Izumi, and Koichi Wada. Space-efficient self-stabilizing counting population protocols on mobile sensor networks. Theoretical Computer Science, 552:99-108, 2014. Google Scholar
  25. Adrian Kosowski and Przemyslaw Uznanski. Brief announcement: Population protocols are fast. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, pages 475-477, 2018. Google Scholar
  26. Anissa Lamani and Masafumi Yamashita. Realization of periodic functions by self-stabilizing population protocols with synchronous handshakes. In Proc. of International Conference on Theory and Practice of Natural Computing, pages 21-33, 2016. Google Scholar
  27. George B Mertzios, Sotiris E Nikoletseas, Christoforos L Raptopoulos, and Paul G Spirakis. Determining majority in networks with local interactions and very small local memory. In International Colloquium on Automata, Languages, and Programming, pages 871-882. Springer, 2014. Google Scholar
  28. Satoshi Murata, Akihiko Konagaya, Satoshi Kobayashi, Hirohide Saito, and Masami Hagiya. Molecular robotics: A new paradigm for artifacts. New Generation Computing, 31(1):27-45, 2013. Google Scholar
  29. Yuichi Sudo, Fukuhito Ooshita, Taisuke Izumi, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. Time-optimal leader election in population protocols. IEEE Transactions on Parallel and Distributed Systems, 2020. Google Scholar
  30. Yuichi Sudo, Fukuhito Ooshita, Hirotsugu Kakugawa, and Toshimitsu Masuzawa. Loosely-stabilizing leader election on arbitrary graphs in population protocols. In International Conference on Principles of Distributed Systems, pages 339-354. Springer, 2014. Google Scholar
  31. Tomoki Umino, Naoki Kitamura, and Taisuke Izumi. Differentiation in population protocols. 6th workshop on biological distributed algorithms(BDA), 2018. Google Scholar
  32. Hiroto Yasumi, Naoki Kitamura, Fukuhito Ooshita, Taisuke Izumi, and Michiko Inoue. A population protocol for uniform k-partition under global fairness. International Journal of Networking and Computing, 9(1):97-110, 2019. Google Scholar
  33. Hiroto Yasumi, Fukuhito Ooshita, and Michiko Inoue. Uniform partition in population protocol model under weak fairness. the 23rd International Conference on Principles of Distributed Systems, 2019. Google Scholar
  34. Hiroto Yasumi, Fukuhito Ooshita, Michiko Inoue, and Sébastien Tixeuil. Uniform bipartition in the population protocol model with arbitrary communication graphs, 2020. URL: http://arxiv.org/abs/2011.08366.
  35. Hiroto Yasumi, Fukuhito Ooshita, Ken'ichi Yamaguchi, and Michiko Inoue. Constant-space population protocols for uniform bipartition. the 21st International Conference on Principles of Distributed Systems, 2017. Google Scholar
  36. Hiroto Yasumi, Fukuhito Ooshita, Ken'ichi Yamaguchi, and Michiko Inoue. Space-optimal population protocols for uniform bipartition under global fairness. IEICE TRANSACTIONS on Information and Systems, 102(3):454-463, 2019. Google Scholar
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact