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A New Synchronous Lower Bound for Set Agreement

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Distributed Computing (DISC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2180))

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Abstract

We have a new proof of the lower bound that k-set agreement requires ⌊f/k⌋ + 1 rounds in a synchronous, message-passing model with f crash failures. The proof involves constructing the set of reachable states, proving that these states are highly connected, and then appealing to a well-known topological result that high connectivity implies that set agreement is impossible. We construct the set of reachable states in an iterative fashion using a round operator that we define, and our proof of connectivity is an inductive proof based on this iterative construction and using simple properties of the round operator. This is the shortest and simplest proof of this lower bound we have seen.

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Author information

Authors and Affiliations

  1. Computer Science Department, Brown University, Providence, RI, 02912, USA

    Maurice Herlihy

  2. Compaq, Cambridge Research Lab, One Cambridge Center, Cambridge, MA, 02142, USA

    Sergio Rajsbaum & Mark Tuttle

Authors
  1. Maurice Herlihy
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  2. Sergio Rajsbaum
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  3. Mark Tuttle
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, 77843-3112, USA

    Jennifer Welch

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© 2001 Springer-Verlag Berlin Heidelberg

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Herlihy, M., Rajsbaum, S., Tuttle, M. (2001). A New Synchronous Lower Bound for Set Agreement. In: Welch, J. (eds) Distributed Computing. DISC 2001. Lecture Notes in Computer Science, vol 2180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45414-4_10

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  • DOI: https://doi.org/10.1007/3-540-45414-4_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42605-9

  • Online ISBN: 978-3-540-45414-4

  • eBook Packages: Springer Book Archive

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