A Nearly Instance-optimal Differentially Private Mechanism for Conjunctive Queries

TL;DR

This paper introduces a new differentially private mechanism for releasing the size of conjunctive and graph pattern queries, achieving near-optimality and improving privacy guarantees over previous methods.

Contribution

It presents the first differentially private mechanism with a strong form of near-instance optimality for query size release under differential privacy.

Findings

Mechanism achieves near-instance optimality.

Provides strong privacy guarantees.

Outperforms existing solutions in utility.

Abstract

Releasing the result size of conjunctive queries and graph pattern queries under differential privacy (DP) has received considerable attention in the literature, but existing solutions do not offer any optimality guarantees. We provide the first DP mechanism for this problem with a fairly strong notion of optimality, which can be considered as a natural relaxation of instance-optimality to a constant.