Differentially Private Distance Query with Asymmetric Noise

TL;DR

This paper introduces a novel edge-based differential privacy mechanism for publishing shortest path distances in social graphs, utilizing asymmetric neighborhoods and smooth sensitivity to improve utility.

Contribution

It proposes the first edge differential privacy approach for distance queries, leveraging asymmetric neighborhoods and smooth sensitivity for better accuracy.

Findings

Reduces error in distance query results to 0.0862

Validates effectiveness on real-world and synthetic datasets

Enhances privacy guarantees with asymmetric neighborhood concepts

Abstract

With the growth of online social services, social information graphs are becoming increasingly complex. Privacy issues related to analyzing or publishing on social graphs are also becoming increasingly serious. Since the shortest paths play an important role in graphs, privately publishing the shortest paths or distances has attracted the attention of researchers. Differential privacy (DP) is an excellent standard for preserving privacy. However, existing works to answer the distance query with the guarantee of DP were almost based on the weight private graph assumption, not on the paths themselves. In this paper, we consider edges as privacy and propose distance publishing mechanisms based on edge DP. To address the issue of utility damage caused by large global sensitivities, we revisit studies related to asymmetric neighborhoods in DP with the observation that the distance query is monotonic in asymmetric neighborhoods. We formally give the definition of asymmetric neighborhoods and propose Individual Asymmetric Differential Privacy with higher privacy guarantees in combination with smooth sensitivity. Then, we introduce two methods to efficiently compute the smooth sensitivity of distance queries in asymmetric neighborhoods. Finally, we validate our scheme using both real-world and synthetic datasets, which can reduce the error to $0.0862$.