Document Open Access Logo

A Topology by Geometrization for Sub-Iterated Immediate Snapshot Message Adversaries and Applications to Set-Agreement

Authors Yannis Coutouly, Emmanuel Godard

PDF
Thumbnail PDF

File

LIPIcs.DISC.2023.15.pdf
  • Filesize: 0.77 MB
  • 20 pages

Document Identifiers

Author Details

Yannis Coutouly
  • Laboratoire d'Informatique et des Systèmes - Université Aix-Marseille, France
  • CNRS, Marseille, France
Emmanuel Godard
  • Laboratoire d'Informatique et des Systèmes - Université Aix-Marseille, France
  • CNRS, Marseille, France

Funding

This work has been funded by ANR project DUCAT - ANR-20-CE48-0006.

Cite As Get BibTex

Yannis Coutouly and Emmanuel Godard. A Topology by Geometrization for Sub-Iterated Immediate Snapshot Message Adversaries and Applications to Set-Agreement. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.DISC.2023.15

Abstract

The Iterated Immediate Snapshot model (IIS) is a central model in the message adversary setting. We consider general message adversaries whose executions are arbitrary subsets of the executions of the IIS message adversary. We present a complete and explicit characterization and lower bounds for solving set-agreement for general sub-IIS message adversaries.
In order to have this characterization, we introduce a new topological approach for such general adversaries, closely associating executions to geometric simplicial complexes. This way, it is possible to define and explicitly construct a topology directly on the considered sets of executions. We believe this topology by geometrization to be of independent interest and a good candidate to investigate distributed computability in general sub-IIS message adversaries, as this could provide both simpler and more powerful ways of using topology for distributed computability.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
Keywords
  • topological methods
  • geometric simplicial complex
  • set-agreement

Metrics

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

References

  1. Yehuda Afek and Eli Gafni. Asynchrony from Synchrony, pages 225-239. Number 7730 in Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2013. Google Scholar
  2. Hagit Attiya, Armando Castañeda, and Thomas Nowak. Topological characterization of task solvability in general models of computation. In Rotem Oshman, editor, Proceedings of the 37th International Symposium on Distributed Computing (DISC'23), volume 281 of LIPICS. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, 2023. Google Scholar
  3. Elizabeth Borowsky and Eli Gafni. Generalized flp impossibility result for t-resilient asynchronous computations. In STOC '93: Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, pages 91-100, New York, NY, USA, 1993. ACM Press. URL: https://doi.org/10.1145/167088.167119.
  4. Elizabeth Borowsky and Eli Gafni. A simple algorithmically reasoned characterization of wait-free computation (extended abstract). In Proceedings of the Sixteenth Annual ACM Symposium on Principles of Distributed Computing, PODC '97, pages 189-198. ACM, 1997. URL: https://doi.org/10.1145/259380.259439.
  5. Arnaud Casteigts, Paola Flocchini, Walter Quattrociocchi, and Nicola Santoro. Time-varying graphs and dynamic networks. Int. J. Parallel Emergent Distributed Syst., 27(5):387-408, 2012. Google Scholar
  6. Bernadette Charron-Bost, Matthias Függer, and Thomas Nowak. Approximate consensus in highly dynamic networks: The role of averaging algorithms. In ICALP (2), volume 9135 of Lecture Notes in Computer Science, pages 528-539. Springer, 2015. Google Scholar
  7. Matthias Függer, Thomas Nowak, and Manfred Schwarz. Tight bounds for asymptotic and approximate consensus. J. ACM, 68(6):46:1-46:35, 2021. Google Scholar
  8. Eli Gafni, Petr Kuznetsov, and Ciprian Manolescu. A generalized asynchronous computability theorem. In Magnús M. Halldórsson and Shlomi Dolev, editors, ACM Symposium on Principles of Distributed Computing, PODC '14, Paris, France, July 15-18, 2014, pages 222-231. ACM, 2014. Google Scholar
  9. Emmanuel Godard and Eloi Perdereau. Back to the coordinated attack problem. Math. Struct. Comput. Sci., 30(10):1089-1113, 2020. Google Scholar
  10. Darald J. Hartfiel. Behavior in Markov set-chains. In Darald J. Hartfiel, editor, Markov Set-Chains, Lecture Notes in Mathematics, pages 91-113. Springer, Berlin, Heidelberg, 1998. URL: https://doi.org/10.1007/BFb0094591.
  11. Allen Hatcher. Algebraic Topology. Cambridge University Press, 2002. Google Scholar
  12. Maurice Herlihy, Dmitry N. Kozlov, and Sergio Rajsbaum. Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, 2013. Google Scholar
  13. Maurice Herlihy, Sergio Rajsbaum, and Michel Raynal. Computability in distributed computing: A tutorial. SIGACT News, 43(3):88-110, 2012. Google Scholar
  14. Maurice Herlihy and Nir Shavit. The topological structure of asynchronous computability. J. ACM, 46(6):858-923, 1999. Google Scholar
  15. Dmitry N. Kozlov. Combinatorial Algebraic Topology, volume 21 of Algorithms and computation in mathematics. Springer, 2008. Google Scholar
  16. Dmitry N. Kozlov. Chromatic subdivision of a simplicial complex. Homology Homotopy Appl., 14(2):197-209, 2012. URL: http://projecteuclid.org/euclid.hha/1355321488.
  17. Petr Kuznetsov, Thibault Rieutord, and Yuan He. An asynchronous computability theorem for fair adversaries. In Calvin Newport and Idit Keidar, editors, Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing, PODC 2018, Egham, United Kingdom, July 23-27, 2018, pages 387-396. ACM, 2018. URL: https://dl.acm.org/citation.cfm?id=3212765.
  18. Nancy A. Lynch. Distributed Algorithms. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1996. Google Scholar
  19. James R. Munkres. Elements Of Algebraic Topology. Addison Wesley Publishing Company, 1984. Google Scholar
  20. Thomas Nowak, Ulrich Schmid, and Kyrill Winkler. Topological characterization of consensus under general message adversaries. In PODC, pages 218-227. ACM, 2019. Google Scholar
  21. J.E. Pin and D. Perrin. Infinite Words, volume 141 of Pure and Applied Mathematics. Elsevier, 2004. Google Scholar
  22. Sergio Rajsbaum. Iterated shared memory models. In Alejandro López-Ortiz, editor, LATIN 2010: Theoretical Informatics, pages 407-416, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg. Google Scholar
  23. Michel Raynal. Set Agreement, pages 1956-1959. Springer New York, New York, NY, 2016. URL: https://doi.org/10.1007/978-1-4939-2864-4_367.
  24. Thibault Rieutord. Combinatorial characterization of asynchronous distributed computability. (Caractérisation combinatoire de la calculabilité distribuée asynchrone). PhD thesis, University of Paris-Saclay, France, 2018. URL: https://tel.archives-ouvertes.fr/tel-02938080.
  25. M. Saks and F. Zaharoglou. "wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. on Computing, 29:1449-1483, 2000. Google Scholar
  26. Emanuel Sperner. Neuer beweis für die invarianz der dimensionszahl und des gebietes. Math. Sem. Univ. Hamburg, 6:265-272, 1928. Google Scholar
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