Peer to Peer Optimistic Collaborative Editing on XML-like trees

Collaborative editing consists in editing a common docu- ment shared by several independent sites. Conflicts occurs when dif- ferent users perform simultaneous uncompatible operations. Centralized systems solve this problem by using locks that prevent some modifica- tions to occur and leave the resolution of conflicts to users. Optimistic peer to peer (P2P) editing doesn't allow locks and uses a Integration Transformation IT that reconciliates conflicting operations and ensures convergence (all copies are identical on each site). Two properties TP1 and TP2, relating the set of allowed operations Op and the transforma- tion IT, have been shown to ensure convergence. The choice of the set Op is crucial to define an integration operation that satisfies TP1 and TP2. Many existing algorithms don't satisfy these properties and are in- correct. No algorithm enjoying both properties is known for strings and little work has been done for XML trees in a pure P2P framework. We focus on editing XML-like trees, i.e. unranked-unordered labeled trees also considered in the Harmony project. We show that no transforma- tion satisfying TP1 and TP2 exists for a first set of operations but that TP1 and TP2 hold for a richer set of operations, provided that some decoration is added to the tree. We show how to combine our approach with any convergent editing process on strings to get a convergent pro- cess. We have implemented our transformation using a P2P algorithm inspired by Ressel et al. whose correctness relies on underlying partial order structure generated by the dependence relation on operations.