Document Open Access Logo

Brief Announcement: Simple and Fast Self-Stabilizing Dynamics for k-Winner-Take-All Computation

Authors Vincenzo Bonifaci , Fabio Galvan

PDF

File

Thumbnail PDF
PDF
LIPIcs.DISC.2026.62.pdf
  • Filesize: 0.73 MB
  • 8 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Computing methodologies → Distributed algorithms
  • Computing methodologies → Neural networks
  • Theory of computation → Bio-inspired optimization
Keywords
  • k-Winner-Take-All
  • network dynamics
  • nature-inspired distributed algorithms
  • electrical flows
  • self-stabilization
  • distributed optimization
  • neural leader election
  • analog computing

Metrics

Abstract

The k-Winner Take All problem consists in identifying the k largest inputs from a collection of input values. We exhibit a simple dynamic network composed of 2n leaky memristor units with a continuous-time dynamics that self-stabilizes and, for any ε > 0, falls within relative distance ε of the k-Winner-Take-All solution on n inputs in time O(ε^{-1} log n).

Cite As Get BibTex

Vincenzo Bonifaci and Fabio Galvan. Brief Announcement: Simple and Fast Self-Stabilizing Dynamics for k-Winner-Take-All Computation. In 40th International Symposium on Distributed Computing (DISC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 397, pp. 62:1-62:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.DISC.2026.62

Author Details

Vincenzo Bonifaci
  • Roma Tre University, Rome, Italy
Fabio Galvan
  • Roma Tre University, Rome, Italy

Funding

This research was partly supported by project ECS 0000024 of the European Commission, Rome Technopole, PNRR grant M4-C2-Inv. 1.5. In particular, FG’s work was funded by Rome Technopole.

Acknowledgements

Work of VB was carried out in association with Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche, Italy.

References

  1. Ruben Becker, Vincenzo Bonifaci, Andreas Karrenbauer, Pavel Kolev, and Kurt Mehlhorn. Two results on slime mold computations. Theoretical Computer Science, 773:79-106, 2019. URL: https://doi.org/10.1016/j.tcs.2018.08.027.
  2. Béla Bollobás. Modern Graph Theory. Springer, 2002. URL: https://doi.org/10.1007/978-1-4612-0619-4.
  3. Vincenzo Bonifaci. On the convergence time of a natural dynamics for linear programming. Algorithmica, 82(2):300-315, 2019. URL: https://doi.org/10.1007/s00453-019-00615-3.
  4. Vincenzo Bonifaci, Kurt Mehlhorn, and Girish Varma. Physarum can compute shortest paths. In Yuval Rabani, editor, Proc. of the 23rd ACM-SIAM Symposium on Discrete Algorithms, pages 233-240, Philadelphia, PA, 2012. SIAM. URL: https://doi.org/10.1137/1.9781611973099.21.
  5. Leon Chua. Memristor, Hodgkin-Huxley, and edge of chaos. In Leon Chua, Georgios Ch. Sirakoulis, and Andrew Adamatzky, editors, Handbook of Memristor Networks, pages 287-314. Springer, 2019. URL: https://doi.org/10.1007/978-3-319-76375-0_10.
  6. L.O. Chua and Sung Mo Kang. Memristive devices and systems. Proceedings of the IEEE, 64(2):209-223, February 1976. URL: https://doi.org/10.1109/PROC.1976.10092.
  7. Robert L. Coultrip, Richard H. Granger, and Gary Lynch. A cortical model of winner-take-all competition via lateral inhibition. Neural Networks, 5(1):47-54, 1992. URL: https://doi.org/10.1016/S0893-6080(05)80006-1.
  8. 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.
  9. Shlomi Dolev. Self-Stabilization. MIT Press, 2000. URL: http://www.cs.bgu.ac.il/%7Edolev/book/book.html.
  10. Shlomi Dolev, Amos Israeli, and Shlomo Moran. Uniform dynamic self-stabilizing leader election. IEEE Trans. Parallel Distributed Syst., 8(4):424-440, 1997. URL: https://doi.org/10.1109/71.588622.
  11. L.V. Ferreira, E. Kaszkurewicz, and A. Bhaya. Synthesis of a k-winners-take-all neural network using linear programming with bounded variables. In Proceedings of the International Joint Conference on Neural Networks, volume 3, pages 2360-2365, 2003. URL: https://doi.org/10.1109/IJCNN.2003.1223781.
  12. Michael J. Fischer and Hong Jiang. Self-stabilizing leader election in networks of finite-state anonymous agents. In Alexander A. Shvartsman, editor, Principles of Distributed Systems, 10th International Conference, OPODIS 2006, Bordeaux, France, December 12-15, 2006, Proceedings, Lecture Notes in Computer Science, pages 395-409. Springer, 2006. URL: https://doi.org/10.1007/11945529_28.
  13. Wulfram Gerstner, Werner M. Kistler, Richard Naud, and Liam Paninski. Neuronal Dynamics. Cambridge University Press, 2014. Google Scholar
  14. Simon Haykin. Neural Networks and Learning Machines. Pearson, 3rd edition, 2009. Google Scholar
  15. John A. Hertz, Anders Krogh, and Richard G. Palmer. Introduction to the Theory of Neural Computation. CRC Press, 1991. Google Scholar
  16. Kentaro Ito, Anders Johansson, Toshiyuki Nakagaki, and Atsushi Tero. Convergence properties for the Physarum solver. arXiv 1101.5249, 2011. URL: https://arxiv.org/abs/1101.5249.
  17. Anders Johannson and James Y. Zou. A slime mold solver for linear programming problems. In S. Barry Cooper, Anuj Dawar, and Benedikt Löwe, editors, How the World Computes - Turing Centenary Conference and 8th Conference on Computability in Europe, CiE 2012, Cambridge, UK, June 18-23, 2012. Proceedings, volume 7318 of Lecture Notes in Computer Science, pages 344-354. Springer, 2012. URL: https://doi.org/10.1007/978-3-642-30870-3_35.
  18. Fabian Kuhn, Thomas Locher, and Roger Wattenhofer. Distributed selection: a missing piece of data aggregation. Commun. ACM, 51(9):93-99, 2008. URL: https://doi.org/10.1145/1378727.1378749.
  19. J. Lazzaro, S. Ryckebusch, M. Mahowald, and C. Mead. Winner-take-all networks of O(n) complexity. In Advances in Neural Information Processing Systems, pages 703-711, 1989. Google Scholar
  20. Shuai Li, MengChu Zhou, Xin Luo, and Zhu-Hong You. Distributed winner-take-all in dynamic networks. IEEE Trans. Autom. Control., 62(2):577-589, 2017. URL: https://doi.org/10.1109/TAC.2016.2578645.
  21. Nancy A. Lynch. Distributed Algorithms. Morgan Kaufmann, 1996. Google Scholar
  22. Nancy A. Lynch, Cameron Musco, and Merav Parter. Computational tradeoffs in biological neural networks: Self-stabilizing winner-take-all networks. In Christos H. Papadimitriou, editor, 8th Innovations in Theoretical Computer Science Conference, ITCS 2017, January 9-11, 2017, Berkeley, CA, USA, volume 67 of LIPIcs, pages 15:1-15:44. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017. URL: https://doi.org/10.4230/LIPIcs.ITCS.2017.15.
  23. Wolfgang Maass. Neural computation with winner-take-all as the only nonlinear operation. In Sara A. Solla, Todd K. Leen, and Klaus-Robert Müller, editors, Advances in Neural Information Processing Systems 12, pages 293-299. The MIT Press, 1999. URL: http://papers.nips.cc/paper/1636-neural-computation-with-winner-take-all-as-the-only-nonlinear-operation.
  24. Wolfgang Maass. On the computational power of winner-take-all. Neural Comput., 12(11):2519-2535, 2000. URL: https://doi.org/10.1162/089976600300014827.
  25. E. Majani, Ruth Erlanson, and Yaser S. Abu-Mostafa. On the K-Winners-Take-All Network. In David S. Touretzky, editor, Advances in Neural Information Processing Systems 1, Denver, Colorado, USA, 1988, pages 634-642. Morgan Kaufmann, 1988. URL: https://proceedings.neurips.cc/paper/1988/file/6c4b761a28b734fe93831e3fb400ce87-Paper.pdf.
  26. Toshiyuki Nakagaki, Hiroyasu Yamada, and Ágota Tóth. Maze-solving by an amoeboid organism. Nature, 407:470, 2000. URL: https://doi.org/10.1038/35035159.
  27. Boaz Patt-Shamir and Allon Shafrir. Approximate distributed top- k queries. Distributed Comput., 21(1):1-22, 2008. URL: https://doi.org/10.1007/S00446-008-0055-3.
  28. Maximilian Riesenhuber and Tomaso Poggio. Hierarchical models of object recognition in cortex. Nature Neuroscience, 2(11):1019-1025, 1999. URL: https://doi.org/10.1038/14819.
  29. Maheshwar Pd. Sah, Hyongsuk Kim, and Leon Chua. Brains are made of memristors. In Leon Chua, Georgios Ch. Sirakoulis, and Andrew Adamatzky, editors, Handbook of Memristor Networks, pages 315-350. Springer, 2019. URL: https://doi.org/10.1007/978-3-319-76375-0_11.
  30. Damian Straszak and Nisheeth K. Vishnoi. Natural algorithms for flow problems. In Robert Krauthgamer, editor, Proceedings of the 27th ACM-SIAM Symposium on Discrete Algorithms, pages 1868-1883. SIAM, 2016. URL: https://doi.org/10.1137/1.9781611974331.ch131.
  31. Damian Straszak and Nisheeth K. Vishnoi. On a natural dynamics for linear programming. In Madhu Sudan, editor, Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science, Cambridge, MA, USA, January 14-16, 2016, page 291. ACM, 2016. URL: https://doi.org/10.1145/2840728.2840762.
  32. Lili Su, Chia-Jung Chang, and Nancy A. Lynch. Spike-based winner-take-all computation: Fundamental limits and order-optimal circuits. Neural Comput., 31(12):2523-2561, 2019. URL: https://doi.org/10.1162/NECO_A_01242.
  33. Atsushi Tero, Seiji Takagi, Tetsu Saigusa, Kentaro Ito, Dan P. Bebber, Mark D. Fricker, Kenji Yumiki, Ryo Kobayashi, and Toshiyuki Nakagaki. Rules for biologically inspired adaptive network design. Science, 327:439-442, 2010. URL: https://doi.org/10.1126/science.1177894.
  34. Jun Wang. Analysis and design of a k-winners-take-all model with a single state variable and the heaviside step activation function. IEEE Trans. Neural Networks, 21(9):1496-1506, 2010. URL: https://doi.org/10.1109/TNN.2010.2052631.
  35. Alan L. Yuille and Davi Geiger. Winner-take-all networks. In Michael A. Arbib, editor, The Handbook of Brain Theory and Neural Networks, pages 1228-1231. MIT Press, 2nd edition, 2003. Google Scholar
  36. Alan L. Yuille and Norberto M. Grzywacz. A winner-take-all mechanism based on presynaptic inhibition feedback. Neural Comput., 1(3):334-347, 1989. URL: https://doi.org/10.1162/NECO.1989.1.3.334.
  37. Yinyan Zhang, Shuai Li, Bin Xu, and Yong Yang. Analysis and design of a distributed k-winners-take-all model. Automatica, 115:108868, 2020. URL: https://doi.org/10.1016/j.automatica.2020.108868.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact