In the process of implementing Cormack’s correction to the dOPT algorithm, I’ve come across several other papers which provide a more complete background of operational transforms and may be of use in the future. They are listed here for sake of documentation – a review of these papers will be provided once I read them carefully.
What follows is an overview of a 1989 journal article by Ellis and Gibbs regarding collaborative editing. It is the origin of the use of operational transforms. For me, it is particularly useful as the dOPT algorithm for reconstructing a cohoerent global state is introduced here. The global state, in the case of the concurrent text editor, is the contents of the document. In more complex scenarios, the state can consist of much more ill-defined properties – in the case of Google Docs, the state would consist of not only the document text, but also the style rendered (bold, italic, etc.). Indeed, much of the work in finally implementing a robust operational transform framework was actually done while developing Google Wave.
Cormack’s 1995 paper shows a flaw in the original dOPT algorithm, in showing that the strength of the algorithm – the completely decentralized nature of the messaging protocol – leads to divergent states across different clients. Fortunately, Cormack outlines a possible way to fix the algorithm, provided that message passing between nodes is retricted to a point-to-point protocol – that is, we can no longer afford the luxury in a network topology of having circular circuits. Fortunately, for our collaborative editing needs, having a p2p network is actually counterintuitive to our needs, and will not inhibit our needs.