Local Distance Query with Differential Privacy

2025-08-07

AI Summary

This paper addresses the challenge of distance queries over graph data under local differential privacy (LDP) in settings without a trusted central data curator. To this end, it proposes two decentralized LDP-compliant distance query methods: one based on synthetic graph construction and another on distributed aggregation of locally perturbed distance vectors. Its key contribution is the first design of an LDP-compliant distance vector randomization mechanism, which jointly employs bit-level perturbation and iterative aggregation over neighboring nodes—thereby preserving global structural information without relying on any centralized coordinator. Theoretical analysis and extensive experiments on real-world datasets demonstrate that the proposed methods achieve significantly lower query error than existing synthetic-graph approaches under strict ε-LDP guarantees, improving utility by 23%–41%, while providing strong privacy protection and practical applicability.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Privacy

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Implementing private distance queries without a trusted curator
• Reducing noise interference in synthetic graph generation
• Capturing global graph structure under local privacy constraints

Innovation

• Generates synthetic graph via randomized responses
• Uses bitwise operations to minimize noise impact
• Aggregates local distance vectors for global accuracy