On Lower Bounds for the Time and the Bit Complexity of Some Probabilistic Distributed Graph Algorithms

(Extended Abstract)
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8327)


This paper concerns probabilistic distributed graph algorithms to solve classical graph problems such as colouring, maximal matching or maximal independent set. We consider anonymous networks (no unique identifiers are available) where vertices communicate by single bit messages. We present a general framework, based on coverings, for proving lower bounds for the bit complexity and thus the execution time to solve these problems. In this way we obtain new proofs of some well known results and some new ones.


Connected Graph Maximal Match Label Graph Port Numbering Election Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ang80]
    Angluin, D.: Local and global properties in networks of processors. In: Proceedings of the 12th Symposium on Theory of Computing, pp. 82–93 (1980)Google Scholar
  2. [BMW94]
    Bodlaender, H.L., Moran, S., Warmuth, M.K.: The distributed bit complexity of the ring: from the anonymous case to the non-anonymous case. Information and Computation 114(2), 34–50 (1994)CrossRefMathSciNetGoogle Scholar
  3. [Bod89]
    Bodlaender, H.-L.: The classification of coverings of processor networks. J. Parallel Distrib. Comput. 6, 166–182 (1989)CrossRefGoogle Scholar
  4. [BV02]
    Boldi, P., Vigna, S.: Fibrations of graphs. Discrete Math. 243, 21–66 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  5. [CM07]
    Chalopin, J., Métivier, Y.: An efficient message passing election algorithm based on Mazurkiewicz’s algorithm. Fundam. Inform. 80(1-3), 221–246 (2007)zbMATHGoogle Scholar
  6. [DMR08]
    Dinitz, Y., Moran, S., Rajsbaum, S.: Bit complexity of breaking and achieving symmetry in chains and rings. Journal of the ACM 55(1) (2008)Google Scholar
  7. [FMRZar]
    Fontaine, A., Métivier, Y., Robson, J.M., Zemmari, A.: The bit complexity of the MIS problem and of the maximal matching problem in anonymous rings. Information and Computation (to appear)Google Scholar
  8. [II86]
    Israeli, A., Itai, A.: A fast and simple randomized parallel algorithm for maximal matching. Information Processing Letters 22, 77–80 (1986)CrossRefMathSciNetGoogle Scholar
  9. [KN99]
    Kushilevitz, E., Nisan, N.: Communication complexity. Cambridge University Press (1999)Google Scholar
  10. [KOSS06]
    Kothapalli, K., Onus, M., Scheideler, C., Schindelhauer, C.: Distributed coloring in \({O}(\sqrt{\log n})\) bit rounds. In: Proceedings of the 20th International Parallel and Distributed Processing Symposium (IPDPS 2006), Rhodes Island, Greece, April 25-29. IEEE (2006)Google Scholar
  11. [MRSDZ10]
    Métivier, Y., Robson, J.M., Saheb-Djahromi, N., Zemmari, A.: About randomised distributed graph colouring and graph partition algorithms. Information and Computation 208(11), 1296–1304 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  12. [MRSDZ11]
    Métivier, Y., Robson, J.M., Saheb-Djahromi, N., Zemmari, A.: An optimal bit complexity randomized distributed MIS algorithm. Distributed Computing 23(5-6), 331–340 (2011)CrossRefzbMATHGoogle Scholar
  13. [Rei32]
    Reidemeister, K.: Einführung in die Kombinatorische Topologie. Vieweg, Brunswick (1932)Google Scholar
  14. [Tel00]
    Tel, G.: Introduction to distributed algorithms. Cambridge University Press (2000)Google Scholar
  15. [Yao79]
    Yao, A.C.: Some complexity questions related to distributed computing. In: Proceedings of the 11th ACM Symposium on Theory of Computing (STOC), pp. 209–213. ACM Press (1979)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.LaBRI UMR CNRS 5800Université de BordeauxTalenceFrance

Personalised recommendations