Reconciling Similar Sets of Data

TL;DR

This paper addresses the problem of efficiently synchronizing two data sets with small differences, especially when differing elements are close in Hamming distance, by establishing bounds and providing algorithms.

Contribution

It introduces bounds and explicit algorithms for data set synchronization considering small symmetric differences and Hamming distance relations.

Findings

Derived bounds on minimal information exchange for synchronization

Provided explicit encoding and decoding algorithms for various cases

Analyzed the impact of Hamming distance on synchronization efficiency

Abstract

In this work, we consider the problem of synchronizing two sets of data where the size of the symmetric difference between the sets is small and, in addition, the elements in the symmetric difference are related through the Hamming distance metric. Upper and lower bounds are derived on the minimum amount of information exchange. Furthermore, explicit encoding and decoding algorithms are provided for many cases.