Lseq

Abstract

Distributed collaborative editing systems allow users to work distributed in time, space and across organizations. Trending distributed collaborative editors such as Google Docs, Etherpad or Git have grown in popularity over the years. A new kind of distributed editors based on a family of distributed data structure replicated on several sites called Conflict-free Replicated Data Type (CRDT for short) appeared recently. This paper considers a CRDT that represents a distributed sequence of basic elements that can be lines, words or characters (sequence CRDT). The possible operations on this sequence are the insertion and the deletion of elements. Compared to the state of the art, this approach is more decentralized and better scales in terms of the number of participants. However, its space complexity is linear with respect to the total number of inserts and the insertion points in the document. This makes the overall performance of such editors dependent on the editing behaviour of users. This paper proposes and models LSEQ, an adaptive allocation strategy for a sequence CRDT. LSEQ achieves in the average a sub-linear spatial-complexity whatever is the editing behaviour. A series of experiments validates LSEQ showing that it outperforms existing approaches.

Verifying strong eventual consistency in distributed systems

“…As with OT, several CRDTs for text documents have been developed, including RGA [Roh et al 2011], Treedoc [Preguiça et al 2009], WOOT [Oster et al 2006b], Logoot , and LSEQ [Nédelec et al 2016[Nédelec et al , 2013. Other datatypes include registers and counters [Shapiro et al 2011a,b], maps [Baquero et al 2016], sets [Bieniusa et al 2012a,b], XML [Martin et al 2010], and JSON trees .…”

A scalable sequence encoding for collaborative editing

“…LSEQ (polyLogarithmic SEQuence) is the name of the proposed allocation function. Our prior works 11,12 empirically showed that LSEQ allocates identifiers with a sublinear upper bound on space complexity. However, we did not provide any complexity analysis to support these observations.…”

“…The results of this hash function must be identical regardless of the editor. 11 For instance, all editors of an editing session use the suballocation function LEFT ‐TO‐RIGHT to choose the paths of size 1. In addition, the choices between the suballocation functions must follow a uniform distribution, for we do not know the future editing behaviors, and we do not want to favor any.…”

“…A sublinear upper bound on the size of identifiers solves the problem and enables real‐time editing in crowdsourcing context. In previous works, 11,12 we proposed an allocation strategy and observed a sublinear upper bound empirically. However, there is no formal proof of such property.…”

“…The contributions of this paper are threefold: Compared to previous works, 11,12 we prove the upper bounds on space and time complexities of LSEQ (polyLogarithmic SEQuence) and the conditions upon which they apply. The size of the identifiers grows up to where I is the number of insertions in the document.…”