R2T: Instance-optimal Truncation for Differentially Private Query Evaluation with Foreign Keys

Abstract

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R2T: Instance-optimal Truncation for Differentially Private Query Evaluation with Foreign Keys

“…In a subsequent work, Tao et al [38] use naive truncation to truncate the tuples with high sensitivity for self-join-free queries and they propose a mechanism to select 𝜏. However, our analysis (see the full version of our paper [15]) shows that the error of their mechanism is Ω(𝐺𝑆 𝑄 /log(𝐺𝑆 𝑄 )) with constant probability, i.e., it is at most a logarithmic-factor better than the naive Laplace mechanism that adds noise of scale 𝐺𝑆 𝑄 . We reduce the dependency on 𝐺𝑆 𝑄 from (near) linear to logarithmic.…”

A Nearly Instance-optimal Differentially Private Mechanism for Conjunctive Queries

“…User-DP is more general than tuple-DP, hence potentially incurring a higher privacy cost. Very recently, a logarithmic-neighborhood optimal mechanism has been proposed for CQs under user-DP [12]. Meanwhile, it has also been shown that 𝑂 (1)-neighborhood optimality is not achievable under user-DP [14] even for the simple query 𝑅 1 (𝑥 1 ) 𝑅 2 (𝑥 1 , 𝑥 2 ) where 𝑅 1 is the primary private relation and 𝑅 2 .𝑥 1 is an FK referencing 𝑅 1 .𝑥 1 .…”

“…In actual implementation, we first compute 𝑇 Ē (I) for all 𝐸 ⊆ 𝐷 𝑖 , 𝐸 ≠ ∅. After that, it only takes 𝑂 (1) time to compute 𝑅𝑆 (I) using formulas (11), (12), and (13). Thus, the concrete computational complexity of 𝑅𝑆 (•) for a CQ 𝑞 is 𝑂 (𝑁 𝑤 max ), where 𝑤 max is the maximum AJAR/FAQ width [3,21] of the residual queries of 𝑞.…”

“…We as before compute L𝑆 (𝑘) (I) by ( 11), (12), and then 𝑅𝑆 (I) by ( 13), but using the new definition of 𝑇 𝐸 (I) with projection. Below we show that 𝑅𝑆 (•) is still a valid 𝜀-DP mechanism and it can be computed efficiently.…”