# Inversion-based Measurement of Data Consistency for Read/Write Registers

## TL;DR

This paper introduces a novel inversion-based method to quantify data consistency violations in distributed storage, addressing limitations of existing approaches by capturing typical disorder patterns among operations.

## Contribution

It proposes the $i$-atomicity model and develops an efficient polynomial verification algorithm for assessing data consistency in distributed systems.

## Key findings

- The inversion-based measure effectively captures typical consistency violations.
- The $i$-atomicity model provides a new way to quantify data disorder.
- The verification algorithm is practical under realistic assumptions.

## Abstract

Both providers and consumers of distributed storage services benefit from the quantification of the severity of consistency violations. However, existing methods fail to capture a typical pattern of violation - the disorder among operations with reference to the ideally strong atomic execution. Such disorder are often seen in Internet applications based on distributed storage services, such as instant messaging. To this end, we use inversions in a permutation with reference to the totally-ordered permutation to measure the consistency of data. The $i$-atomicity model is proposed and a (pseudo-)polynomial verification algorithm for a restricted type of histories is proposed. The basic idea of the verification algorithm is brute-force search of the permutation with less than $i$ inversions, which requires exponential cost. Reasonable assumptions abstracted from applications scenarios can be leveraged to prune the search space, which yields an efficient polynomial verification algorithm.