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Gracefully Degrading Consensus and k-Set Agreement in Directed Dynamic Networks

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Networked Systems (NETYS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 9466))

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Abstract

We present (This work has been supported the Austrian Science Fund (FWF) project P26436 (SIC) and S11405 (RiSE).) the first consensus/k-set agreement algorithm for synchronous dynamic networks with unidirectional links, controlled by an omniscient message adversary, which automatically adapts to the actual network properties in a run: If the network is sufficiently well-connected, it solves consensus, while it degrades gracefully to general k-set agreement in less well-connected communication graphs. The actual number k of system-wide decision values is determined by the number of certain vertex-stable root components occurring in a run, which are strongly connected components without incoming links from outside. Related impossibility results reveal that our condition is reasonably close to the solvability border for k-set agreement.

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Notes

  1. 1.

    It is important to note, however, that the network properties required by our algorithm to reach k decision values need not involve k isolated partitions: Obviously, k isolated partitions in the communication graph also imply k root components, but k root components do not imply a partitioning of the communication graph into k components — it may still be weakly connected.

  2. 2.

    That is, by convention, we also call a VSRC \(D\)-bounded if its duration is too short to be interesting.

  3. 3.

    Working out the intricacies of relating our message adversaries to failure detectors (in the spirit of [14]) is part of our current research.

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Authors and Affiliations

  1. EPFL, Lausanne, Switzerland

    Martin Biely

  2. National University of Singapore, Singapore, Singapore

    Peter Robinson

  3. ECS Group, TU Wien, Vienna, Austria

    Ulrich Schmid, Manfred Schwarz & Kyrill Winkler

Authors
  1. Martin Biely
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  2. Peter Robinson
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  3. Ulrich Schmid
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  4. Manfred Schwarz
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  5. Kyrill Winkler
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Corresponding author

Correspondence to Manfred Schwarz .

Editor information

Editors and Affiliations

  1. Université Paris Diderot, Paris Cedex 13, France

    Ahmed Bouajjani

  2. Université Paris Diderot, Paris Cedex 13, France

    Hugues Fauconnier

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Biely, M., Robinson, P., Schmid, U., Schwarz, M., Winkler, K. (2015). Gracefully Degrading Consensus and k-Set Agreement in Directed Dynamic Networks. In: Bouajjani, A., Fauconnier, H. (eds) Networked Systems . NETYS 2015. Lecture Notes in Computer Science(), vol 9466. Springer, Cham. https://doi.org/10.1007/978-3-319-26850-7_8

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  • DOI: https://doi.org/10.1007/978-3-319-26850-7_8

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