Brief Announcement: Randomized Consensus: Common Coins Are not the Holy Grail!

Achour Mostéfaoui, Matthieu Perrin, Julien Weibel

Abstract:

This paper studies the round complexity of randomized binary consensus in crash-prone asynchronous distributed systems. While the
Consensus problem cannot be solved deterministically, Ben-Or and
Rabin showed that randomization allows solving the problem with
probability $1$. Moreover, while local coins may need an exponential
number of rounds in $𝑛$, a common coin that delivers the same random sequence to all processes allows termination within a constant
mean number of rounds. This paper studies the round complexity and the optimality for different coins. Surprisingly, while the
common coin is optimal when $𝑡 > 𝑛/3$, it is not when $𝑡 \leq 𝑛/3$.