Optimal amortized distributed consensus
Are randomized consensus algorithms more powerful than deterministic ones? Seemingly so, since randomized algorithms exist that reach consensus in expected constant number of rounds, whereas the deterministic counterparts are constrained by the r ≥ t + 1 lower bound in the number of communication rounds, where t is the maximum number of faults to be tolerated.
In this paper, however, we study the behavior of deterministic algorithms when consensus is repeatedly needed, say k times. We show that it is possible to achieve consensus with the optimal number of processors (n > 3t), and optimal amortized cost in all other measures: the number of communication rounds r*, the maximal message size m*, and the total bit complexity b*.
More specifically, we achieve the following amortized bounds for k consensus instances: r*=O(1 + t/k), b*=O(t2+ t1/k), and m*=O(1 + t2/k). When k ≥ t2, then r* and m* are O(1) and b*=O(t2) which is optimal.
KeywordsMessage Size Consensus Problem Consensus Algorithm Communication Round Byzantine Agreement
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