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)

Abstract

We present tradeoffs between time complexity t, bit complexity b, and message complexity m. Two communication parties can exchange Θ(mlog(tb/m2) + 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 tc (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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

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

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