The main question is the following:
When designing a system supporting atomic broadcast, can it be proved theoretically that the performance & scalability dimensions (i.e. latency, throughput, dataset size) of the system are limited by the performance of a single node?

To give an example:
A system based on partitioned-logs, like Apache Kafka, can provide ordering guarantees in a single partition, but it can't provide any ordering guarantees between different partitions. However, this gives Kafka the capability to scale to extremely large datasets. I was contemplating whether it would be possible to create a system that could provide the ordering guarantee for the whole dataset, while also allowing the dataset's size to increase in the same quasi-linear way.

My speculative answer to this is no for the following reason:
It's been proved that the atomic broadcast problem is equivalent to the consensus problem [1]. Based on the fact that the consensus problem requires an elected leader, which drives the consensus process, I concluded that the scaling capabilities of such a system is limited by the resources of a single node.

Are there any flaws in my thinking ?

[1]: https://en.wikipedia.org/wiki/Atomic_broadcast#Equivalent_to_Consensus


2 Answers 2


Your argument for "no" is flawed, for two reasons:

  • When we say that X reduces to Y, we mean that a solution to Y is one way to solve X. But there might be other ways to solve X that don't rely on solving Y.

  • Some protocols for consensus elect a leader, but that doesn't necessarily imply that all approaches to solve consensus require electing a leader. (For example: consider Bitcoin. No leader, but it arguably solves a consensus kind of problem.)

  • $\begingroup$ Thanks for the answer! Regarding the first point, if X and Y problems are equivalent (as is the case actually), would I still be able to do that jump in my inference ? Regarding the second point, that's a nice insight, I had never thought of distributed ledgers from this perspective, I'll definitely have a look into it. $\endgroup$
    – Dimos
    Mar 9, 2018 at 10:27

I've already accepted D.W.'s answer above, but posting some of my later findings for reference of people that end up reading this question:

  • As implied in the question, all consensus algorithms (e.g. Paxos, Raft, Chandra–Toueg) have an elected leader (even a temporary one) which is driving the convergence to the consensus result. This aspect creates a somewhat central bottleneck that would make a quasi-linear scaling extremely challenging. For instance, adding nodes to the system to increase performance would increase coordination, thus preventing big performance increases
  • With regards to Bitcoin and other similar (blockchain) approaches, it does not require an elected leader, but it solves a different version of the consensus problem. More specifically, Bitcoin achieves probabilistic (not deterministic) consensus.

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