Certification of Compact Low-Stretch Routing Schemes

Authors Alkida Balliu, Pierre Fraigniaud

Thumbnail PDF


  • Filesize: 0.58 MB
  • 16 pages

Document Identifiers

Author Details

Alkida Balliu
Pierre Fraigniaud

Cite AsGet BibTex

Alkida Balliu and Pierre Fraigniaud. Certification of Compact Low-Stretch Routing Schemes. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


On the one hand, the correctness of routing protocols in networks is an issue of utmost importance for guaranteeing the delivery of messages from any source to any target. On the other hand, a large collection of routing schemes have been proposed during the last two decades, with the objective of transmitting messages along short routes, while keeping the routing tables small. Regrettably, all these schemes share the property that an adversary may modify the content of the routing tables with the objective of, e.g., blocking the delivery of messages between some pairs of nodes, without being detected by any node. In this paper, we present a simple certification mechanism which enables the nodes to locally detect any alteration of their routing tables. In particular, we show how to locally verify the stretch 3 routing scheme by Thorup and Zwick [SPAA 2001] by adding certificates of ~O(sqrt(n)) bits at each node in n-node networks, that is, by keeping the memory size of the same order of magnitude as the original routing tables. We also propose a new name-independent routing scheme using routing tables of size ~O(sqrt(n)) bits. This new routing scheme can be locally verified using certificates on ~O(sqrt(n)) bits. Its stretch is 3 if using handshaking, and 5 otherwise.
  • Distributed verification
  • compact routing
  • local computing


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


  1. Ittai Abraham, Cyril Gavoille, and Dahlia Malkhi. On space-stretch trade-offs: upper bounds. In SPAA 2006: Proceedings of the 18th Annual ACM Symposium on Parallelism in Algorithms and Architectures, Cambridge, Massachusetts, USA, July 30 - August 2, 2006, pages 217-224, 2006. Google Scholar
  2. Ittai Abraham, Cyril Gavoille, Dahlia Malkhi, Noam Nisan, and Mikkel Thorup. Compact name-independent routing with minimum stretch. In SPAA 2004: Proceedings of the Sixteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures, June 27-30, 2004, Barcelona, Spain, pages 20-24, 2004. Google Scholar
  3. Marta Arias, Lenore Cowen, Kofi A. Laing, Rajmohan Rajaraman, and Orjeta Taka. Compact routing with name independence. In SPAA 2003: Proceedings of the Fifteenth Annual ACM Symposium on Parallelism in Algorithms and Architectures, June 7-9, 2003, San Diego, California, USA (part of FCRC 2003), pages 184-192, 2003. Google Scholar
  4. Baruch Awerbuch, Amotz Bar-Noy, Nathan Linial, and David Peleg. Compact distributed data structures for adaptive routing (extended abstract). In Proceedings of the 21st Annual ACM Symposium on Theory of Computing, May 14-17, 1989, Seattle, Washigton, USA, pages 479-489, 1989. Google Scholar
  5. Baruch Awerbuch and David Peleg. Sparse partitions (extended abstract). In 31st Annual Symposium on Foundations of Computer Science, St. Louis, Missouri, USA, October 22-24, 1990, Volume II, pages 503-513, 1990. Google Scholar
  6. Alkida Balliu and Pierre Fraigniaud. Certification of compact low-stretch routing schemes. In 31st International Symposium on Distributed Computing, DISC 2017, October 16-20, 2017, Vienna, Austria, 2017. Google Scholar
  7. Mor Baruch, Pierre Fraigniaud, and Boaz Patt-Shamir. Randomized proof-labeling schemes. In Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing, PODC 2015, Donostia-San Sebastián, Spain, July 21 - 23, 2015, pages 315-324, 2015. Google Scholar
  8. Shiri Chechik. Compact routing schemes with improved stretch. In ACM Symposium on Principles of Distributed Computing, PODC'13, Montreal, QC, Canada, July 22-24, 2013, pages 33-41, 2013. Google Scholar
  9. Niels Ferguson, Bruce Schneier, and Tadayoshi Kohno. Cryptography Engineering: Design Principles and Practical Applications. Wiley Publishing, 2010. Google Scholar
  10. Laurent Feuilloley and Pierre Fraigniaud. Survey of distributed decision. Bulletin of the EATCS, 119, 2016. Google Scholar
  11. Pierre Fraigniaud and Cyril Gavoille. Routing in trees. In Automata, Languages and Programming, 28th International Colloquium, ICALP 2001, Crete, Greece, July 8-12, 2001, Proceedings, pages 757-772, 2001. Google Scholar
  12. Pierre Fraigniaud and Cyril Gavoille. A space lower bound for routing in trees. In STACS 2002, 19th Annual Symposium on Theoretical Aspects of Computer Science, Antibes - Juan les Pins, France, March 14-16, 2002, Proceedings, pages 65-75, 2002. Google Scholar
  13. Pierre Fraigniaud, Amos Korman, and David Peleg. Towards a complexity theory for local distributed computing. J. ACM, 60(5):35, 2013. Google Scholar
  14. Klaus-Tycho Förster, Thomas Lüdi, Jochen Seidel, and Roger Wattenhofer. Local Checkability, No Strings Attached: (A)cyclicity, Reachability, Loop Free Updates in SDNs. In Theoretical Computer Science (TCS), November 2016. Google Scholar
  15. Cyril Gavoille. Routing in distributed networks: overview and open problems. SIGACT News, 32(1):36-52, 2001. Google Scholar
  16. Cyril Gavoille and Marc Gengler. Space-efficiency for routing schemes of stretch factor three. J. Parallel Distrib. Comput., 61(5):679-687, 2001. Google Scholar
  17. Cyril Gavoille and David Peleg. Compact and localized distributed data structures. Distributed Computing, 16(2-3):111-120, 2003. Google Scholar
  18. Cyril Gavoille and Stephane Perennes. Memory requirements for routing in distributed networks (extended abstract). In Proceedings of the Fifteenth Annual ACM Symposium on Principles of Distributed Computing, Philadelphia, Pennsylvania, USA, May 23-26, 1996, pages 125-133, 1996. Google Scholar
  19. Mika Göös and Jukka Suomela. Locally checkable proofs in distributed computing. Theory of Computing, 12(1):1-33, 2016. Google Scholar
  20. Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. Distributed Computing, 22(4):215-233, 2010. Google Scholar
  21. David Peleg and Eli Upfal. A tradeoff between space and efficiency for routing tables (extended abstract). In Proceedings of the 20th Annual ACM Symposium on Theory of Computing, May 2-4, 1988, Chicago, Illinois, USA, pages 43-52, 1988. Google Scholar
  22. Nicola Santoro and Ramez Khatib. Labelling and implicit routing in networks. Comput. J., 28(1):5-8, 1985. Google Scholar
  23. Stefan Schmid and Jukka Suomela. Exploiting locality in distributed SDN control. In Proceedings of the Second ACM SIGCOMM Workshop on Hot Topics in Software Defined Networking, HotSDN 2013, The Chinese University of Hong Kong, Hong Kong, China, Friday, August 16, 2013, pages 121-126, 2013. Google Scholar
  24. Mikkel Thorup and Uri Zwick. Compact routing schemes. In SPAA, pages 1-10, 2001. Google Scholar
  25. Andrew Chi-Chih Yao. Some complexity questions related to distributive computing (preliminary report). In Proceedings of the 11h Annual ACM Symposium on Theory of Computing, April 30 - May 2, 1979, Atlanta, Georgia, USA, pages 209-213, 1979. Google Scholar
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