We show that the `optimal’ use of the parallel composition theorem
corresponds to finding the size of the largest subset of queries that `overlap’
on the data domain, a quantity we call the emph{maximum overlap} of the
queries. It has previously been shown that a certain instance of this problem,
formulated in terms of determining the sensitivity of the queries, is NP-hard,
but also that it is possible to use graph-theoretic algorithms, such as finding
the maximum clique, to approximate query sensitivity. In this paper, we
consider a significant generalization of the aforementioned instance which
encompasses both a wider range of differentially private mechanisms and a
broader class of queries. We show that for a particular class of predicate
queries, determining if they are disjoint can be done in time polynomial in the
number of attributes. For this class, we show that the maximum overlap problem
remains NP-hard as a function of the number of queries. However, we show that
efficient approximate solutions exist by relating maximum overlap to the clique
and chromatic numbers of a certain graph determined by the queries. The link to
chromatic number allows us to use more efficient approximate algorithms, which
cannot be done for the clique number as it may underestimate the privacy
budget. Our approach is defined in the general setting of $f$-differential
privacy, which subsumes standard pure differential privacy and Gaussian
differential privacy. We prove the parallel composition theorem for
$f$-differential privacy. We evaluate our approach on synthetic and real-world
data sets of queries. We show that the approach can scale to large domain sizes
(up to $10^{20000}$), and that its application can reduce the noise added to
query answers by up to 60%.

360 Mobile Vision - 360mobilevision.com North & South Carolina Security products and Systems Installations for Commercial and Residential - $55 Hourly Rate. ACCESS CONTROL, INTRUSION ALARM, ACCESS CONTROLLED GATES, INTERCOMS AND CCTV INSTALL OR REPAIR 360 Mobile Vision - 360mobilevision.com is committed to excellence in every aspect of our business. We uphold a standard of integrity bound by fairness, honesty and personal responsibility. Our distinction is the quality of service we bring to our customers. Accurate knowledge of our trade combined with ability is what makes us true professionals. Above all, we are watchful of our customers interests, and make their concerns the basis of our business.

By admin