On the Power of Graphical Reconfigurable Circuits

Authors Yuval Emek , Yuval Gil , Noga Harlev



PDF
Thumbnail PDF

File

LIPIcs.DISC.2024.22.pdf
  • Filesize: 0.75 MB
  • 16 pages

Document Identifiers

Author Details

Yuval Emek
  • Technion - Israel Institute of Technology, Haifa, Israel
Yuval Gil
  • Technion - Israel Institute of Technology, Haifa, Israel
Noga Harlev
  • Technion - Israel Institute of Technology, Haifa, Israel

Cite AsGet BibTex

Yuval Emek, Yuval Gil, and Noga Harlev. On the Power of Graphical Reconfigurable Circuits. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.DISC.2024.22

Abstract

We introduce the graphical reconfigurable circuits (GRC) model as an abstraction for distributed graph algorithms whose communication scheme is based on local mechanisms that collectively construct long-range reconfigurable channels (this is an extension to general graphs of a distributed computational model recently introduced by Feldmann et al. (JCB 2022) for hexagonal grids). The crux of the GRC model lies in its modest assumptions: (1) the individual nodes are computationally weak, with state space bounded independently of any global graph parameter; and (2) the reconfigurable communication channels are highly restrictive, only carrying information-less signals (a.k.a. beeps). Despite these modest assumptions, we prove that GRC algorithms can solve many important distributed tasks efficiently, i.e., in polylogarithmic time. On the negative side, we establish various runtime lower bounds, proving that for other tasks, GRC algorithms (if they exist) are doomed to be slow.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • graphical reconfigurable circuits
  • bounded uniformity
  • beeping

Metrics

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

References

  1. Yehuda Afek, Noga Alon, Ziv Bar-Joseph, Alejandro Cornejo, Bernhard Haeupler, and Fabian Kuhn. Beeping a maximal independent set. Distributed Comput., 26(4):195-208, 2013. URL: https://doi.org/10.1007/S00446-012-0175-7.
  2. Dana Angluin. Local and global properties in networks of processors (extended abstract). In Raymond E. Miller, Seymour Ginsburg, Walter A. Burkhard, and Richard J. Lipton, editors, Proceedings of the 12th Annual ACM Symposium on Theory of Computing (STOC), pages 82-93. ACM, 1980. URL: https://doi.org/10.1145/800141.804655.
  3. Otakar Boruvka. Contribution to the solution of a problem of economical construction of electrical networks. Elektronickỳ Obzor, 15:153-154, 1926. Google Scholar
  4. Alejandro Cornejo and Fabian Kuhn. Deploying wireless networks with beeps. In Nancy A. Lynch and Alexander A. Shvartsman, editors, Distributed Computing, 24th International Symposium, DISC 2010, Cambridge, MA, USA, September 13-15, 2010. Proceedings, volume 6343 of Lecture Notes in Computer Science, pages 148-162. Springer, 2010. URL: https://doi.org/10.1007/978-3-642-15763-9_15.
  5. Michael Elkin and Ofer Neiman. Efficient algorithms for constructing very sparse spanners and emulators. ACM Trans. Algorithms, 15(1):4:1-4:29, 2019. URL: https://doi.org/10.1145/3274651.
  6. Yuval Emek, Yuval Gil, and Noga Harlev. On the power of graphical reconfigurable circuits, 2024. URL: https://arxiv.org/abs/2408.10761.
  7. Michael Feldmann, Andreas Padalkin, Christian Scheideler, and Shlomi Dolev. Coordinating amoebots via reconfigurable circuits. Journal of Computational Biology, 29(4):317-343, 2022. URL: https://doi.org/10.1089/CMB.2021.0363.
  8. Roland Flury and Roger Wattenhofer. Slotted programming for sensor networks. In Tarek F. Abdelzaher, Thiemo Voigt, and Adam Wolisz, editors, Proceedings of the 9th International Conference on Information Processing in Sensor Networks, IPSN 2010, April 12-16, 2010, Stockholm, Sweden, pages 24-34. ACM, 2010. URL: https://doi.org/10.1145/1791212.1791216.
  9. Sebastian Forster, Martin Grösbacher, and Tijn de Vos. An improved random shift algorithm for spanners and low diameter decompositions. In Quentin Bramas, Vincent Gramoli, and Alessia Milani, editors, 25th International Conference on Principles of Distributed Systems, OPODIS 2021, December 13-15, 2021, Strasbourg, France, volume 217 of LIPIcs, pages 16:1-16:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPICS.OPODIS.2021.16.
  10. Lauri Hella, Matti Järvisalo, Antti Kuusisto, Juhana Laurinharju, Tuomo Lempiäinen, Kerkko Luosto, Jukka Suomela, and Jonni Virtema. Weak models of distributed computing, with connections to modal logic. Distributed Comput., 28(1):31-53, 2015. URL: https://doi.org/10.1007/S00446-013-0202-3.
  11. Gary L. Miller, Richard Peng, Adrian Vladu, and Shen Chen Xu. Improved parallel algorithms for spanners and hopsets. In Guy E. Blelloch and Kunal Agrawal, editors, Proceedings of the 27th ACM on Symposium on Parallelism in Algorithms and Architectures, SPAA 2015, Portland, OR, USA, June 13-15, 2015, pages 192-201. ACM, 2015. URL: https://doi.org/10.1145/2755573.2755574.
  12. Gary L. Miller, Richard Peng, and Shen Chen Xu. Parallel graph decompositions using random shifts. In Guy E. Blelloch and Berthold Vöcking, editors, 25th ACM Symposium on Parallelism in Algorithms and Architectures, SPAA '13, Montreal, QC, Canada - July 23 - 25, 2013, pages 196-203. ACM, 2013. URL: https://doi.org/10.1145/2486159.2486180.
  13. Andreas Padalkin and Christian Scheideler. Polylogarithmic time algorithms for shortest path forests in programmable matter. In ACM Symposium on Principles of Distributed Computing (PODC), 2024. To appear. Google Scholar
  14. Andreas Padalkin, Christian Scheideler, and Daniel Warner. The structural power of reconfigurable circuits in the amoebot model. In Thomas E. Ouldridge and Shelley F. J. Wickham, editors, 28th International Conference on DNA Computing and Molecular Programming, DNA 28, August 8-12, 2022, University of New Mexico, Albuquerque, New Mexico, USA, volume 238 of LIPIcs, pages 8:1-8:22. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.DNA.28.8.
  15. David Peleg. Distributed computing: a locality-sensitive approach. SIAM, 2000. Google Scholar
  16. David Peleg and Vitaly Rubinovich. A near-tight lower bound on the time complexity of distributed minimum-weight spanning tree construction. SIAM J. Comput., 30(5):1427-1442, 2000. URL: https://doi.org/10.1137/S0097539700369740.
  17. Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, and Roger Wattenhofer. Distributed verification and hardness of distributed approximation. SIAM J. Comput., 41(5):1235-1265, 2012. URL: https://doi.org/10.1137/11085178X.
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