Common Contracts

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

March 12th, 2018

• Filed
  March 12th, 2018

We study1 distributed agreement in synchronous directed dynamic networks, where an omniscient message adversary controls the presence/absence of communication links. We prove that consensus is impossible under a message adversary that guarantees weak connectivity only, and introduce eventually vertex-stable source components (VSSCs) as a means for circumventing this impossibility: A VSSC(k, d) message adversary guarantees that, eventually, there is an interval of d consecutive rounds where every communication graph contains at most k strongly connected components consisting of the same processes (with possibly varying interconnect topology), which have no incoming links from outside processes. We present a consensus algorithm that works correctly under a VSSC(1, 4E + 2) message adversary, where E is the dynamic network depth. Our algorithm maintains local estimates of the communication graphs, and applies techniques for detecting network stability and univalent system configurations. S