Operational Transformation (OT) is a consistency maintenance technique for collaborative editing systems-a special class of distributed applications for supporting human-computer-human interaction and collaboration over communication networks. The theory of causality has been the foundation of all prior OT systems, but it is inadequate to meet essential OT requirements in functionality and correctness. In this paper, we analyze the limitation of the causality theory, propose a novel theory of operation context as the new foundation for OT systems, and present a new OT algorithm-Context-based OT (COT)-which provides uniform and efficient solutions to both consistency maintenance and undo problems. The COT algorithm has been implemented and used for supporting a range of novel collaborative applications. The context theory and context vectors are potentially applicable to other distributed computing applications.

Context-Based Operational Transformation in Distributed Collaborative Editing Systems

Operational Transformation (OT) is a technique for consistency maintenance and group undo, and is being applied to an increasing number of collaborative applications The theoretical foundation for OT is crucial in determining its capability to solve existing and new problems, as well as the quality of those solutions The theory of causality has been the foundation of all prior OT systems, but it is inadequate to capture essential correctness requirements Past research had invented various patches to work around this problem, resulting in increasingly intricate and complicated OT algorithms After having designed, implemented, and experimented with a series of OT algorithms, we reflected on what had been learned and set out to develop a new theoretical framework for better understanding and resolving OT problems, reducing its complexity, and supporting its continual evolution In this paper, we report the main results of this effort: the theory of operation context and the COT (Context-based OT) algorithm The COT algorithm is capable of supporting both do and undo of any operations at anytime, without requiring transformation functions to preserve Reversibility Property, Convergence Property 2, Inverse Properties 2 and 3 The COT algorithm is not only simpler and more efficient than prior OT control algorithms, but also simplifies the design of transformation functions We have implemented the COT algorithm in a generic collaboration engine and used it for supporting a range of novel collaborative applications

Operation context and context-based operational transformation

Operational transformation (OT) as a consistency control method has been well accepted in group editors. With OT, the users can edit any part of a shared document at any time and local responsiveness is not sensitive to communication latencies. However, established theoretical frameworks for developing OT algorithms either require transformation functions to work in all possible cases, which complicates the design of transformation functions, or include an under-formalized condition of intention preservation, which results in algorithms that cannot be formally proved and must be fixed over time to address newly discovered counterexamples. To address those limitations, this paper proposes an alternative framework, called admissibility-based transformation (ABT), that is theoretically based on formalized, provable correctness criteria and practically no longer requires transformation functions to work under all conditions. Compared to previous approaches, ABT simplifies the design and proofs of OT algorithms.

An Admissibility-Based Operational Transformation Framework for Collaborative Editing Systems

Group editors allow a group of distributed human users to edit a shared multimedia document at the same time over a computer network. Consistency control in this environment must not only guarantee convergence of replicated data, but also attempt to preserve intentions of operations. Operational transformation (OT) is a well-established method for optimistic consistency control in this context and has drawn continuing research attention since 1989. However, counterexamples to previous works have often been identified despite the significant progress made on this topic over the past 15 years. This paper analyzes the root of correctness problems in OT and establishes a novel operational transformation framework for developing OT algorithms and proving their correctness

A New Operational Transformation Framework for Real-Time Group Editors

Operational transformation (OT) is a responsive and nonblocking concurrency control method widely-accepted in group editors. Correctness and performance are the basis of usefulness and usability of OT-based group editors. However, the correctness of previous OT algorithms depends on conditions that are very difficult to verify. In this paper we propose a novel landmark-based transformation (LBT) approach, its correctness no longer depending on those conditions and thus easy to prove. In addition, we give an example algorithm that significantly outperforms a state-of-the-art OT algorithm. This work reveals a more practical approach to developing OT algorithms.

A landmark-based transformation approach to concurrency control in group editors

Traditional concurrency control methods such as locking and serialization are not suitable for distributed interactive applications that demand fast local response. Operational transformation (OT) is the standard solution to concurrency control and consistency maintenance in group editors, an important class of interactive groupware applications. It generally trades consistency for local responsiveness, because human users can often tolerate temporary inconsistencies but do not like their interactions be lost or nondeterministically blocked. This paper presents a time interval based operational transformation algorithm (TIBOT) that overcomes the various limitations of previous related work. Our approach guarantees content convergence and is significantly more simple and efficient than existing approaches. This is achieved in a pure replicated architecture by using a linear clock and by posing some constraints on communication that are reasonable for the application domain.

Chengzheng Sun

Papers

A time interval based consistency control algorithm for interactive groupware applications