The using Directed Acyclic Graph to store ledger information for a cryptocurrency was first proposed by Sergio Demian Lerner in 2012 and formalised by him in 2015.
https://bitslog.wordpress.com/2015/09/11/dagcoin/
A working implementation was first release by Anton Churyumov was in 2016 – Byteball.
IOTA does use the Directed Acyclic Graph but there are several people in the crypto community who have concerns and unanswered questions and time frames for resolving the issue that at the time of writing mid 2017 only 33% of the hashpower of the network would be required to rewrite the IOTA “tangle” (their implementation of Sergio Demian Lerner Directed Acyclic Graph.)
https://medium.com/@ercwl/iota-is-centralized-6289246e7b4d
