It is well-known that consensus (one-set agreement) and total order broadcast are equivalent in asynchronous systems prone to process crash failures. Considering wait-free systems, this article addresses and answers the following question: which is the communication abstraction that "captures" k-set agreement? To this end, it introduces a new broadcast communication abstraction, called k-BO-Broadcast, which restricts the disagreement on the local deliveries of the messages that have been broadcast (1-BO-Broadcast boils down to total order broadcast). Hence, in this context, k=1 is not a special number, but only the first integer in an increasing integer sequence. This establishes a new "correspondence" between distributed agreement problems and communication abstractions, which enriches our understanding of the relations linking fundamental issues of fault-tolerant distributed computing.
Cite
@article{arxiv.1705.04835,
title = {Which Broadcast Abstraction Captures $k$-Set Agreement?},
author = {Damien Imbs and Achour Mostéfaoui and Matthieu Perrin and Michel Raynal},
journal= {arXiv preprint arXiv:1705.04835},
year = {2017}
}