Decision optimal early-stopping k-set agreement in synchronous systems prone to send omission failures

The k-set agreement problem is a generalization of the consensus problem: each process proposes a value, and each non-faulty process has to decide a value such that a decided value is a proposed value, and no more than k different values are decided. This paper focuses on the k-set agreement problem in the context of synchronous systems where up to t < n processes can experience crash or send omission failures (n being the total number of processes). The paper presents a k-set agreement protocol for this failure model (the first to our knowledge) which has two main outstanding features. (1) It provides the following early deciding and stopping property: no process decides or halts after the round min(└f/k┘ + 2, └t/k┘ + 1) where f is the number of actual crashes (0 ≤ f ≤ t). (2) It is decision-optimal. This new optimality criterion, suited to the omission failure model, concerns the number of processes that decide, namely, the protocol forces all the processes that do not crash to decide (regardless of whether they commit omission faults or not). It is noteworthy that each of these properties (early deciding/stopping vs decision-optimality) is not obtained at the detriment of the other. Last but not least, the protocol enjoys another first-class property, namely, simplicity.