  The goal of this article is to extend the ideas concerning Bracha-Toueg
asynchronous Byzantine Fault Tolerant consensus algorithm and Baird's Hashgraph
consensus. We propose a family of atomic broadcast algorithms, which Hashgraph
consensus is closely related to. We also do preliminary comparative algorithm
speed analysis which shows that some members of the family seriously outperform
Hashgraph consensus. These algorithms can also be readily used as a base of
proof-of-stake consensuses. In appendix we provide an extension of Hashgraph
gossip protocol, which efficiently handles byzantine fault information exchange
between nodes.
