Trading Bit, Message, and Time Complexity of Distributed Algorithms

  • Johannes Schneider
  • Roger Wattenhofer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6950)


We present tradeoffs between time complexity t, bit complexity b, and message complexity m. Two communication parties can exchange Θ(mlog(tb/m 2) + b) bits of information for \(m < \sqrt{bt}\) and Θ(b) for \(m \geq \sqrt{bt}\). This allows to derive lower bounds on the time complexity for distributed algorithms as we demonstrate for the MIS and the coloring problems. We reduce the bit-complexity of the state-of-the art O(Δ) coloring algorithm without changing its time and message complexity. We also give techniques for several problems that require a time increase of t c (for an arbitrary constant c) to cut both bit and message complexity by Ω(logt). This improves on the traditional time-coding technique which does not allow to cut message complexity.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barenboim, L., Elkin, M.: Distributed (δ + 1)-coloring in linear (in δ) time. In: Symposium on Theory of Computing(STOC) (2009)Google Scholar
  2. 2.
    Barenboim, L., Elkin, M.: Deterministic distributed vertex coloring in polylogarithmic time. In: Symp. on Principles of Distributed Computing (PODC) (2010)Google Scholar
  3. 3.
    Dinitz, Y., Moran, S., Rajsbaum, S.: Bit complexity of breaking and achieving symmetry in chains and rings. J. ACM (2008)Google Scholar
  4. 4.
    Fraigniaud, P., Gavoille, C., Ilcinkas, D., Pelc, A.: Distributed computing with advice: information sensitivity of graph coloring. In: Distributed Computing (2009)Google Scholar
  5. 5.
    Fraigniaud, P., Giakkoupis, G.: On the bit communication complexity of randomized rumor spreading. In: SPAA (2010)Google Scholar
  6. 6.
    Frederickson, G.N., Lynch, N.A.: Electing a leader in a synchronous ring. J. ACM 34(1) (1987)Google Scholar
  7. 7.
    Kothapalli, K., Scheideler, C., Onus, M., Schindelhauer, C.: Distributed coloring in \(O(\sqrt{\log n})\) bit rounds. In: International Parallel & Distributed Processing Symposium, IPDPS (2006)Google Scholar
  8. 8.
    Kuhn, F.: Weak Graph Coloring: Distributed Algorithms and Applications. In: Parallelism in Algorithms and Architectures, SPAA (2009)Google Scholar
  9. 9.
    Kuhn, F., Moscibroda, T., Wattenhofer, R.: What Cannot Be Computed Locally! In: Symposium on Principles of Distributed Computing, PODC (2005)Google Scholar
  10. 10.
    Kuhn, F., Wattenhofer, R.: On the Complexity of Distributed Graph Coloring. In: Symp. on Principles of Distributed Computing, PODC (2006)Google Scholar
  11. 11.
    Kushilevitz, E., Nisan, N.: Communication complexity. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar
  12. 12.
    Linial, N.: Locality in Distributed Graph Algorithms. SIAM Journal on Computing 21(1), 193–201 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lotker, Z., Patt-Shamir, B., Pettie, S.: Improved distributed approximate matching. In: SPAA (2008)Google Scholar
  14. 14.
    Luby, M.: A Simple Parallel Algorithm for the Maximal Independent Set Problem. SIAM Journal on Computing 15, 1036–1053 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Métivier, Y., Robson, J.M., Nasser, S.-D., Zemmar, A.: An optimal bit complexity randomized distributed MIS algorithm. In: Kutten, S., Žerovnik, J. (eds.) SIROCCO 2009. LNCS, vol. 5869, pp. 323–337. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Nisan, N., Wigderson, A.: Rounds in communication complexity revisited. SIAM J. Comput. 22(1) (1993)Google Scholar
  17. 17.
    Santoro, N.: Design and Analysis of Distributed Algorithms. Wiley-Interscience, Hoboken (2006)CrossRefzbMATHGoogle Scholar
  18. 18.
    Schneider, J., Wattenhofer, R.: A New Technique For Distributed Symmetry Breaking. In: Symp. on Principles of Distributed Computing, PODC (2010)Google Scholar
  19. 19.
    Schneider, J., Wattenhofer, R.: Distributed Coloring Depending on the Chromatic Number or the Neighborhood Growth. In: Kosowski, A., Yamashita, M. (eds.) SIROCCO 2011. LNCS, vol. 6796, pp. 246–257. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  20. 20.
    Schneider, J., Wattenhofer, R.: Poster Abstract: Message Position Modulation for Power Saving and Increased Bandwidth in Sensor Networks. In: 10th ACM/IEEE International Conference on Information Processing in Sensor Networks, IPSN (2011)Google Scholar
  21. 21.
    Schneider, J., Wattenhofer, R.: Trading Bit, Message, and Time Complexity of Distributed Algorithms. TIK Technical Report 339 (2011),

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Johannes Schneider
    • 1
  • Roger Wattenhofer
    • 1
  1. 1.Computer Engineering and Networks LaboratoryETH ZurichZurichSwitzerland

Personalised recommendations