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