# A Differentially Private Algorithm for Range Queries on Trajectories

## TL;DR

This paper introduces a new differentially private algorithm for range queries on trajectory data that adaptively adds noise, achieving lower error and higher utility than existing methods by considering data and query awareness.

## Contribution

It presents the first data- and query-aware differential privacy method for trajectory range queries that adaptively partitions data to improve accuracy.

## Key findings

- Achieves significantly lower error compared to state-of-the-art methods.
- Effectively maintains trajectory data consistency while ensuring privacy.
- Demonstrates high accuracy and efficiency on real and synthetic datasets.

## Abstract

We propose a novel algorithm to ensure $\epsilon$-differential privacy for answering range queries on trajectory data. In order to guarantee privacy, differential privacy mechanisms add noise to either data or query, thus introducing errors to queries made and potentially decreasing the utility of information. In contrast to the state-of-the-art, our method achieves significantly lower error as it is the first data- and query-aware approach for such queries. The key challenge for answering range queries on trajectory data privately is to ensure an accurate count. Simply representing a trajectory as a set instead of \emph{sequence} of points will generally lead to highly inaccurate query answers as it ignores the sequential dependency of location points in trajectories, i.e., will violate the consistency of trajectory data. Furthermore, trajectories are generally unevenly distributed across a city and adding noise uniformly will generally lead to a poor utility. To achieve differential privacy, our algorithm adaptively adds noise to the input data according to the given query set. It first privately partitions the data space into uniform regions and computes the traffic density of each region. The regions and their densities, in addition to the given query set, are then used to estimate the distribution of trajectories over the queried space, which ensures high accuracy for the given query set. We show the accuracy and efficiency of our algorithm using extensive empirical evaluations on real and synthetic data sets.