k-Set Agreement and Renaming in the Presence of Contention-Related Crash Failures
Résumé
A new notion of process failure explicitly related to contention has recently been introduced by one of the authors (NETYS 2018). More precisely, given a predefined contention threshold λ, this notion considers the executions in which process crashes are restricted to occur only when process contention is smaller than or equal to λ. If crashes occur after contention bypassed λ, there are no correctness guarantees (e.g., termination is not guaranteed). It was shown that, when λ = n − 1, consensus can be solved in an n-process asynchronous read/write system despite the crash of one process, thereby circumventing the well-known FLP impossibility result. Furthermore, it was shown that when λ = n − k and k ≥ 2, k-set agreement can be solved despite the crash of 2k − 2 processes.
This paper considers two types of process crash failures: "λ-constrained" crash failures (as previously defined), and classical crash failures (that we call "any time" failures). It presents two algorithms suited to these types of failures. The first algorithm solves k-set agreement, where k = m+f , in the presence of t = 2m + f − 1 crash failures, 2m of them being (n − k)-constrained failures, and (f − 1) being any time failures. The second algorithm solves (n + f)-renaming in the presence of t = m + f crash failures, m of them being (n − t − 1)-constrained failures, and f being any time failures. It follows that the differentiation between λ-constrained crash failures and any time crash failures enlarges the space of executions in which the impossibility of k-set agreement and renaming in the presence of asynchrony and process crashes can be circumvented. In addition to its behavioral properties, both algorithms have a noteworthy first class property, namely, their simplicity.
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