Concurrency Effects Over Variable-size Identifiers in Distributed Collaborative Editing

Distributed collaborative editors such as Google Docs or Etherpad allow to distribute the work across time, space and organizations. In this paper, we focus on distributed collaborative editors based on the Conflict-free Replicated Data Type approach (CRDT). CRDTs encompass a set of well-known data types such as sets, graphs, sequences, etc. CRDTs for sequences model a document as a set of elements (character, line, paragraph, etc.) with unique identifiers, providing two commutative update operations: insert and delete. The identifiers of elements can be either of fixed-size or variable-size. Recently, a strategy for assigning variable-size identifiers called LSEQ has been proposed for CRDTs for sequences. LSEQ lowers the space complexity of variable-size identifiers CRDTs from linear to sub-linear. While experiments show that it works locally, it fails to provide this bound with multiple users and latency. In this paper, we propose h-LSEQ, an improvement of LSEQ that preserves its space complexity among multiple collaborators, regardless of the latency. Ultimately, this improvement allows to safely build distributed collaborative editors based on CRDTs. We validate our approach with simulations involving latency and multiple users.