Abstract: User data collection and analysis with local differential privacy has attracted considerable attention in recent years. The trade-off among the domain size of user data, encoding method, and perturbation method directly constrains the accuracy of spatial range query. To remedy the deficiency caused by the current encoding and perturbating method, this paper employs grid and quadtree to propose an efficient solution, called GT-R, to answer spatial range query. GT-R uses a uniform grid to decompose the data domain, and generate unit sized regions. Based on these regions, an indexing quadtree is built. And then each user encodes his/her data with the quadtree shared from server, and runs the optimal randomized response on each node of the sampled level in the quadtree and reports the sampled level along with the perturbed value. The server accumulates reports from users to reconstruct a quadtree comprising sum of reports from all users. Besides, to boost the accuracy of range query, the server relies on post-processing skill for consistency on the frequency of each node. GT-R method is compared with existing methods on the large-scale real datasets. The experimental results show that GT-R outperforms its competitors, achieves the accurate results of spatial range query.

Key words: local differential privacy, spatial range query, grid decomposition, randomized response, constrained inference