Abstract
A condition C is a set of input vectors to a problem. A class of conditions that allow to solve k-set agreement in spite of f crashes in an asynchronous system is identified. A k-set agreement protocol that is always safe is described: it is guaranteed to terminate when the input vector belongs to C and it always decides on at most k different values, even if the input vector does not belong to C. While there are simple solutions when f < k, it is known that the k-set agreement problem has no solution when f ≥ k. Thus, the paper identifies classes of conditions that allow to solve this problem even when f ≥ k. The paper gives evidence that these are the only conditions that allow to solve set agreement, by proving the wait-free case. Two natural concrete conditions that belong to such a class are described. Finally, a more efficient k-set agreement protocol with only linear complexity (does not use snapshots), for any C that allows to solve consensus, when k ≤ f/(n - f) + 1 is presented. This shows how to trade fault-tolerance for agreement precision using the condition based approach.
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Mostéfaoui, A., Rajsbaum, S., Raynal, M., Roy, M. (2002). Condition-Based Protocols for Set Agreement Problems. In: Malkhi, D. (eds) Distributed Computing. DISC 2002. Lecture Notes in Computer Science, vol 2508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36108-1_4
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DOI: https://doi.org/10.1007/3-540-36108-1_4
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