Differentially Private Distance Query with Asymmetric Noise

2025-01-14

AI Summary

This paper addresses shortest-distance queries on social network graphs under edge-level privacy protection. It proposes the first differentially private (DP) framework for exact distance release under edge differential privacy (Edge-DP), departing from the conventional “private-weight graph” assumption. The method introduces an asymmetric neighborhood modeling scheme and an individual asymmetric DP model, integrated with smooth sensitivity analysis and a monotonicity-driven noise injection mechanism—substantially reducing privacy budget consumption. Evaluated on real-world and synthetic datasets, it achieves a mean query error of 0.0862, outperforming state-of-the-art approaches. Key contributions are: (1) the first Edge-DP shortest-distance release mechanism targeting graph structure—not edge weights; (2) asymmetric neighborhood characterization to capture heterogeneous local influence of nodes, improving the utility–accuracy trade-off; and (3) theoretical guarantees ensuring simultaneous optimization of strong privacy preservation and practical query performance.

Technology Category

• Machine Learning: Privacy
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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 $0.0862$.

Problem

• Privacy Protection
• Social Network Graphs
• Accurate Querying

Innovation

• Edge-based Differential Privacy
• Asymmetric Neighborhood
• Distance Query Sensitivity Smoothing