Gracefully degrading consensus/ Sample Clauses

Gracefully degrading consensus/ k-set agreement In this section, we provide a k-set agreement algorithm and prove that it works correctly under the message adversary VSSCD,H (n, 3D + H) + MAJINF(k), i.e., the conjunction of Definitions 15 and 19. Note that the algorithm needs to know D, but neither n nor H. It consists of a “generic” k-set agreement algorithm, which relies on the network approximation algorithm of Section 5.1 for locally detecting vertex- stable source components and a function GetLock that extracts candidate decision values from history information. Our implementation of GetLock uses a vector-clock-like mechanism for maintaining “causally consistent” history information, which can be guaranteed to lead to proper candidate values thanks to VSSCD,H (n, 3D + H) + MAJINF(k). In sharp contrast to classic k-set agreement algorithms, the algorithm is k-universal, i.e., the parameter k does not appear in its code. Rather, the number of system-wide decision values is determined by the number of (certain) 2D + 1-VSSCs occurring in the particular run. As a consequence, if the network partitions into k weakly connected components, for example,9 all processes in a component obtain the same decision value. On the other hand, if the network remains well-connected, the algorithm guarantees a unique decision value system-wide.
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