Local Distance Query with Differential Privacy

TL;DR

This paper introduces two methods for performing differentially private distance queries in graphs under Local Differential Privacy, with the second method effectively capturing global structure through local aggregations.

Contribution

The paper presents the first LDP-based distance query method that captures global graph structure via local distance vector aggregation, improving utility.

Findings

The second approach outperforms synthetic graph methods in utility.

The proposed method effectively captures global graph structure.

Experimental results validate the theoretical analysis.

Abstract

Differential Privacy (DP) is commonly employed to safeguard graph analysis or publishing. Distance, a critical factor in graph analysis, is typically handled using curator DP, where a trusted curator holds the complete neighbor lists of all vertices and answers queries privately. However, in many real-world scenarios, such a curator may not be present, posing a significant challenge for implementing differentially private distance queries under Local Differential Privacy (LDP). This paper proposes two approaches to address this challenge. The first approach generates a synthetic graph by randomizing responses and applies bitwise operations to reduce noise interference. However, like other synthetic graph methods, this approach suffers from low utility. To overcome this limitation, we propose a second approach, the first LDP method specifically designed for distance queries, which captures the global graph structure by continuously aggregating local distance vectors from neighboring vertices. This process enables the accurate updating of global distances. We demonstrate the effectiveness of our method through comprehensive theoretical analysis and experimental evaluations on real-world datasets.