Document Open Access Logo

The Topology of Local Computing in Networks

Authors Pierre Fraigniaud, Ami Paz

Thumbnail PDF


  • Filesize: 1.09 MB
  • 18 pages

Document Identifiers

Author Details

Pierre Fraigniaud
  • Institut de Recherche en Informatique Fondamentale, CNRS, Université de Paris, France
Ami Paz
  • Faculty of Computer Science, Universität Wien, Austria


Both authors are thankful to Juho Hirvonen for his help with the figures.

Cite AsGet BibTex

Pierre Fraigniaud and Ami Paz. The Topology of Local Computing in Networks. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 128:1-128:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed algebraic topology. In both cases, the considered computational model generally assumes communication via shared objects (typically a shared memory consisting of a collection of read-write registers), or message-passing enabling direct communication between any pair of processes. Our paper is concerned with network computing, where the processes are located at the nodes of a network, and communicate by exchanging messages along the edges of that network (only neighboring processes can communicate directly). Applying the topological approach for verification in network computing is a considerable challenge, mainly because the presence of identifiers assigned to the nodes yields protocol complexes whose size grows exponentially with the size of the underlying network. However, many of the problems studied in this context are of local nature, and their definitions do not depend on the identifiers or on the size of the network. We leverage this independence in order to meet the above challenge, and present local protocol complexes, whose sizes do not depend on the size of the network. As an application of the design of "compacted" protocol complexes, we reformulate the celebrated lower bound of Ω(log^*n) rounds for 3-coloring the n-node ring, in the algebraic topology framework.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Distributed computing
  • distributed graph algorithms
  • combinatorial topology


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


  1. Hagit Attiya, Armando Castañeda, Maurice Herlihy, and Ami Paz. Bounds on the step and namespace complexity of renaming. SIAM J. Comput., 48(1):1-32, 2019. URL:
  2. Alkida Balliu, Sebastian Brandt, Juho Hirvonen, Dennis Olivetti, Mikaël Rabie, and Jukka Suomela. Lower bounds for maximal matchings and maximal independent sets. In 60th IEEE Annual Symposium on Foundations of Computer Science (FOCS), pages 481-497, 2019. URL:
  3. Sebastian Brandt. An automatic speedup theorem for distributed problems. In ACM Symposium on Principles of Distributed Computing (PODC), pages 379-388, 2019. URL:
  4. Armando Castañeda, Pierre Fraigniaud, Ami Paz, Sergio Rajsbaum, Matthieu Roy, and Corentin Travers. A topological perspective on distributed network algorithms. In 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO), LNCS 11639, pages 3-18. Springer, 2019. URL:
  5. Armando Castañeda and Sergio Rajsbaum. New combinatorial topology bounds for renaming: the lower bound. Distributed Computing, 22(5-6):287-301, 2010. URL:
  6. Armando Castañeda and Sergio Rajsbaum. New combinatorial topology bounds for renaming: The upper bound. J. ACM, 59(1):3:1-3:49, 2012. URL:
  7. Lisbeth Fajstrup, Eric Goubault, Emmanuel Haucourt, Samuel Mimram, and Martin Raussen. Directed Algebraic Topology and Concurrency. Springer, 2016. Google Scholar
  8. Michael J. Fischer, Nancy A. Lynch, and Mike Paterson. Impossibility of distributed consensus with one faulty process. J. ACM, 32(2):374-382, 1985. URL:
  9. Pierre Fraigniaud and Ami Paz. The topology of local computing in networks. Tech. Report arXiv abs/2003.03255, 2020. URL:
  10. Éric Goubault, Samuel Mimram, and Christine Tasson. Geometric and combinatorial views on asynchronous computability. Distributed Computing, 31(4):289-316, 2018. URL:
  11. Maurice Herlihy, Dmitry N. Kozlov, and Sergio Rajsbaum. Distributed Computing Through Combinatorial Topology. Morgan Kaufmann, 2013. URL:
  12. Maurice Herlihy and Nir Shavit. The topological structure of asynchronous computability. J. ACM, 46(6):858-923, 1999. URL:
  13. Juhana Laurinharju and Jukka Suomela. Brief announcement: Linial’s lower bound made easy. In ACM Symposium on Principles of Distributed Computing (PODC), pages 377-378, 2014. URL:
  14. Ronald L.Graham, Bruce L. Rothschild, Joel H. Spencer, and József Solymosi. Ramsey Theory. John Wiley and Sons, 2015. Google Scholar
  15. Nathan Linial. Locality in distributed graph algorithms. SIAM J. Comput., 21(1):193-201, 1992. URL:
  16. Moni Naor and Larry J. Stockmeyer. What can be computed locally? SIAM J. Comput., 24(6):1259-1277, 1995. URL:
  17. David Peleg. Distributed Computing: A Locality-Sensitive Approach. SIAM, 2001. Google Scholar
  18. Michael E. Saks and Fotios Zaharoglou. Wait-free k-set agreement is impossible: The topology of public knowledge. SIAM J. Comput., 29(5):1449-1483, 2000. URL:
  19. Jukka Suomela. Survey of local algorithms. ACM Comput. Surv., 45(2):24:1-24:40, 2013. URL:
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail