Brief announcement: gracefully degrading consensus and k-set agreement under dynamic link failures

We present a k-set agreement algorithm for synchronous dynamic distributed systems with unidirectional links controlled by an omniscient adversary. Our algorithm automatically adapts to the actual network properties: If the network is sufficiently well-connected, it solves consensus, while degrading gracefully to general k-set agreement in less well-behaved runs. The algorithm is oblivious to the maximum number of system-wide decision values k, which is bounded by the number of certain strongly connected components occurring in the dynamically changing network in a run. Related impossibility results reveal that this bound is close to the solvability border for k-set agreement. To the best of our knowledge, this is the first consensus algorithm that degrades in a graceful way in a dynamic network.