Average Long-Lived Memoryless Consensus: The Three-Value Case

  • Ivan Rapaport
  • Eric Rémila
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6058)


We study strategies that minimize the instability of a fault-tolerant consensus system. More precisely, we find the strategy than minimizes the number of output changes over a random walk sequence of input vectors (where each component of the vector corresponds to a particular sensor reading). We analyze the case where each sensor can read three possible inputs. The proof of this result appears to be much more complex than the proof of the binary case (previous work). In the binary case the problem can be reduced to a minimal cut in a graph. We succeed in three dimensions by using the fact that an auxiliary graph (projected graph) is planar. For four and higher dimensions this auxiliary graph is not planar anymore and the problem remains open.


Line Segment Input Vector Consensus Function Median Axis Sensor Reading 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ivan Rapaport
    • 1
  • Eric Rémila
    • 2
  1. 1.DIM-CMM (UMI 2807 CNRS), Universidad de ChileSantiagoChile
  2. 2.Université de Lyon, LIP (UMR 5668 CNRS-ENS, Université Lyon 1)Lyon Cedex 7France

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