Maintaining constraints expressed as formulas in collaborative systems

Constraints allow users to declare relationships among objects and let the constraint systems maintain and satisfy these relationships. Formulas have been adopted to express constraints in a wide variety of single-user applications, because of their simplicity, efficiency and manageability. The needs and benefits of supporting formula-defined constraints in collaborative environments have long been recognized. However, maintaining both constraints and consistency in the presence of concurrency in collaborative systems is a challenge. In these systems, users may concurrently define formulas, which could result in that different formulas are defined to express the same object attribute at different sites. In this article, we discuss the issues and techniques in maintaining formula-defined constraints in collaborative systems. In particular, we also proposed a method that is able to maintain both constraints and system consistency in concurrent environments based on the existing consistency maintenance approaches. This method extends the application of these approaches from collaborative systems without constraint to systems that support formulas. The proposed method has been applied to implement a collaborative Visio system, called CoVisio, which leverages single-user Microsoft Visio for multi-user collaboration. Specific issues related to CoVisio are also discussed in detail.