Brief announcement: pareto optimal solutions to consensus and set consensus

A protocol P is Pareto-optimal if no protocol Q can decide as fast as P for all adversaries, while allowing at least one process to decide strictly earlier, in at least one instance. Pareto optimal protocols cannot be improved upon. We present the first Pareto-optimal solutions to consensus and k-set consensus for synchronous message-passing with crashes failures. Our k-set consensus protocol strictly dominates all known solutions, and our results expose errors in [1, 7, 8, 12]. Our proofs of Pareto optimality are completely constructive, and are devoid of any topological arguments or reductions.

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