Exploiting Metric Structure for Efficient Private Query Release

TL;DR

This paper introduces efficient algorithms for privately answering distance queries on databases in metric spaces, enabling accurate, privacy-preserving responses in both online and offline settings, and overcoming previous computational hardness barriers.

Contribution

The paper presents the first efficient algorithms for private distance query release on metric space databases, applicable to both online and offline scenarios.

Findings

Algorithms run efficiently in database size and space dimension.

Applicable to both online and offline query release settings.

Circumvents known hardness results for generic linear queries.

Abstract

We consider the problem of privately answering queries defined on databases which are collections of points belonging to some metric space. We give simple, computationally efficient algorithms for answering distance queries defined over an arbitrary metric. Distance queries are specified by points in the metric space, and ask for the average distance from the query point to the points contained in the database, according to the specified metric. Our algorithms run efficiently in the database size and the dimension of the space, and operate in both the online query release setting, and the offline setting in which they must in polynomial time generate a fixed data structure which can answer all queries of interest. This represents one of the first subclasses of linear queries for which efficient algorithms are known for the private query release problem, circumventing known hardness results for generic linear queries.