Answering Spatial Density Queries Under Local Differential Privacy

Spatial density queries are fundamental in many geospatial data analysis and crowdsourcing tasks. However, answering spatial density queries may violate users’ privacy by exposing their locations to an untrusted data collector. In this article, we propose a solution for answering spatial density queries under local differential privacy (LDP), a state-of-the-art privacy protection standard. Our solution consists of four main steps: 1) partitioning; 2) finding sensitivity; 3) user-side noisy response computation; and 4) server-side estimation. For the first step, we propose and analyze three basic partitioning strategies, and based on our analysis, we design an improved strategy called Advanced Partitioning. For the second step, we adapt graph-based modeling of query sets from the centralized differential privacy literature. Advanced Partitioning also leverages and extends this technique by formulating the partitioning problem using vertex coloring. For the third and fourth steps, in addition to adapting two popular LDP protocols (GRR and RAPPOR), we propose a novel extension for the optimized unary encoding protocol. Our new protocol (OBE) is not only applicable to our problem but can also be used in other LDP problems with bitvector encodings. Finally, we perform an extensive experimental evaluation of different partitioning strategies and protocols using multiple real-world data sets. Results show that Advanced Partitioning and OBE yield the lowest error, demonstrating the superiority of our proposed methods.