Gradecast is a simple three-round algorithm presented by Feldman and Micali. The current work presents a very simple synchronous algorithm that utilized Gradecast to achieve Byzantine agreement. Two small variations of the presented algorithm lead to improved algorithms for solving the Approximate agreement problem and the Multi-consensus problem. An optimal approximate agreement algorithm was presented by Fekete, which supports up to 1 n Byzantine nodes and has message complexity of O(n k ), where n is the number of nodes and k is the number of rounds. Our solution to the approximate agreement problem is optimal,
Multi Consensus: The algorithm Multi-Consensus presented in @cite_17 solves @math sequential consensuses within @math rounds and is resilient to @math . However, @cite_17 assumes that the starts of the different @math consensuses are synchronized, a property that cannot be ensured when a consensus stops early. In the current paper we show how to adapt ideas from @cite_5 such that our solution does not require synchronized starts of the different consensuses.
@cite_5 @cite_17
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In a seminal paper, Feldman and Micali show an n-party Byzantine agreement protocol in the plain model that tolerates t 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.