Towards Synchronizing Linear Collaborative Objects with Operational Transformation

A collaborative object represents a data type (such as a text document or a filesystem) designed to be shared by multiple geographically separated users. Data replication is a technology to improve performance and availability of data in distributed systems. Indeed, each user has a local copy of the shared objects, upon which he may perform updates. Locally executed updates are then transmitted to the other users. This replication potentially leads, however, to divergent (i.e. different) copies. In this respect, Operational Transformation (OT) algorithms are applied for achieving convergence of all copies, i.e. all users view the same objects. Using these algorithms users can apply the same set of updates but possibly in different orders since the convergence should be ensured in all cases. However, achieving convergence with the OT approach is still a critical and challenging issue. In this paper, we address an open convergence problem when the shared data has a linear structure such as list, text, ordered XML tree, etc. We analyze the source of this problem and we propose a generic solution with its formal correctness.