Fundamental Limits of Database Alignment

TL;DR

This paper introduces a new measure called cycle mutual information to determine the fundamental limits of aligning correlated databases, providing both theoretical thresholds and an efficient algorithm for exact recovery.

Contribution

The paper proposes cycle mutual information as a novel measure and establishes its role in the fundamental limits of database alignment, along with an efficient matching algorithm.

Findings

Cycle mutual information characterizes the possibility of exact database alignment.

An efficient algorithm achieves the information-theoretic threshold for alignment.

The measure has operational significance in determining recoverability.

Abstract

We consider the problem of aligning a pair of databases with correlated entries. We introduce a new measure of correlation in a joint distribution that we call cycle mutual information. This measure has operational significance: it determines whether exact recovery of the correspondence between database entries is possible for any algorithm. Additionally, there is an efficient algorithm for database alignment that achieves this information theoretic threshold.