Abstract
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.
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Schneider, J., Wattenhofer, R. (2011). Trading Bit, Message, and Time Complexity of Distributed Algorithms. In: Peleg, D. (eds) Distributed Computing. DISC 2011. Lecture Notes in Computer Science, vol 6950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24100-0_4
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DOI: https://doi.org/10.1007/978-3-642-24100-0_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24099-7
Online ISBN: 978-3-642-24100-0
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