Algebra of Data Reconciliation

TL;DR

This paper presents an algebraic framework for data reconciliation in distributed systems, enabling efficient synchronization of diverging data replicas through maximal subsequence propagation and algebraic properties.

Contribution

It introduces a complete command set, an update detection algorithm, and an algebraic model that guarantees a unique maximal reconciliation solution.

Findings

The command set is functionally complete.

An efficient algorithm for maximal reconciliation is developed.

The model guarantees a unique maximal solution.

Abstract

With distributed computing and mobile applications becoming ever more prevalent, synchronizing diverging replicas of the same data is a common problem. Reconciliation -- bringing two replicas of the same data structure as close as possible without overriding local changes -- is investigated in an algebraic model. Our approach is to consider two sequences of simple commands that describe the changes in the replicas compared to the original structure, and then determine the maximal subsequences of each that can be propagated to the other. The proposed command set is shown to be functionally complete, and an update detection algorithm is presented which produces a command sequence transforming the original data structure into the replica while traversing both simultaneously. Syntactical characterization is provided in terms of a rewriting system for semantically equivalent command sequences. Algebraic properties of sequence pairs that are applicable to the same data structure are investigated. Based on these results the reconciliation problem is shown to have a unique maximal solution. In addition, syntactical properties of the maximal solution allow for an efficient algorithm that produces it.