An Optimized String Transformation Algorithm for Real-Time Group Editors

Operational transformation (OT) is an optimistic consistency control method for supporting collaboration over high-latency networks. The technique lies in the heart of many recent products such as Google Wave. It replicates the shared data and allows the users to concurrently modify any part of a shared document in a nonblocking manner. Most of the published results only support two characterwise primitives and take $O(|H|^2)$ or even longer time to integrate one remote characterwise operation, where $H$ is the operation history. However, as the history grows long and operations are integrated in batches, the high complexity can make an algorithm easily exceed the 100 ms responsiveness threshold that is critical for interactive applications. This paper proposes a new OT algorithm that supports string primitives and reduces the time complexity to $O(|H|)$. The result can be used in a range of parallel and distributed applications that can be abstracted as realtime group editors.