We show that it is possible to significantly improve the accuracy of a general class of histogram queries while satisfying differential privacy. Our approach carefully chooses a set of queries to evaluate, and then exploits consistency constraints that should hold over the noisy output. In a postprocessing phase, we compute the consistent input most likely to have produced the noisy output. The final output is differentially-private and consistent, but in addition, it is often much more accurate. We show, both theoretically and experimentally, that these techniques can be used for estimating the degree sequence of a graph very precisely, and for computing a histogram that can support arbitrary range queries accurately.

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N.B. This is the full version of the conference paper published as [12]. This version includes an Appendix with proofs and additional results, and corrects a few typographical errors discovered after publication. It also adds an improvement in the error bounds achieved under ( , δ)-differential privacy, included as Theorem 5. ABSTRACTDifferential privacy is a robust privacy standard that has been successfully applied to a range of data analysis tasks. But despite much recent work, optimal strategies for answering a collection of related queries are not known.We propose the matrix mechanism, a new algorithm for answering a workload of predicate counting queries. Given a workload, the mechanism requests answers to a different set of queries, called a query strategy, which are answered using the standard Laplace mechanism. Noisy answers to the workload queries are then derived from the noisy answers to the strategy queries. This two stage process can result in a more complex correlated noise distribution that preserves differential privacy but increases accuracy.We provide a formal analysis of the error of query answers produced by the mechanism and investigate the problem of computing the optimal query strategy in support of a given workload. We show this problem can be formulated as a rank-constrained semidefinite program. Finally, we analyze two seemingly distinct techniques, whose similar behavior is explained by viewing them as instances of the matrix mechanism.

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We identify privacy risks associated with releasing network data sets and provide an algorithm that mitigates those risks. A network consists of entities connected by links representing relations such as friendship, communication, or shared activity. Maintaining privacy when publishing networked data is uniquely challenging because an individual's network context can be used to identify them even if other identifying information is removed. In this paper, we quantify the privacy risks associated with three classes of attacks on the privacy of individuals in networks, based on the knowledge used by the adversary. We show that the risks of these attacks vary greatly based on network structure and size. We propose a novel approach to anonymizing network data that models aggregate network structure and then allows samples to be drawn from that model. The approach guarantees anonymity for network entities while preserving the ability to estimate a wide variety of network measures with relatively little bias.

We identify privacy risks associated with releasing network data sets and provide an algorithm that mitigates those risks. A network consists of entities connected by links representing relations such as friendship, communication, or shared activity. Maintaining privacy when publishing networked data is uniquely challenging because an individual's network context can be used to identify them even if other identifying information is removed. In this paper, we quantify the privacy risks associated with three classes of attacks on the privacy of individuals in networks, based on the knowledge used by the adversary. We show that the risks of these attacks vary greatly based on network structure and size. We propose a novel approach to anonymizing network data that models aggregate network structure and then allows samples to be drawn from that model. The approach guarantees anonymity for network entities while preserving the ability to estimate a wide variety of network measures with relatively little bias.

XPath is a language for navigating an XML document and selecting a set of element nodes. XPath expressions are used to query XML data, describe key constraints, express transformations, and reference elements in remote documents. This article studies the containment and equivalence problems for a fragment of the XPath query language, with applications in all these contexts.In particular, we study a class of XPath queries that contain branching, label wildcards and can express descendant relationships between nodes. Prior work has shown that languages that combine any two of these three features have efficient containment algorithms. However, we show that for the combination of features, containment is coNP-complete. We provide a sound and complete algorithm for containment that runs in exponential time, and study parameterized PTIME special cases. While we identify one parameterized class of queries for which containment can be decided efficiently, we also show that even with some bounded parameters, containment remains coNP-complete. In response to these negative results, we describe a sound algorithm that is efficient for all queries, but may return false negatives in some cases.

We describe a new algorithm for answering a given set of range queries under -differential privacy which often achieves substantially lower error than competing methods. Our algorithm satisfies differential privacy by adding noise that is adapted to the input data and to the given query set. We first privately learn a partitioning of the domain into buckets that suit the input data well. Then we privately estimate counts for each bucket, doing so in a manner well-suited for the given query set. Since the performance of the algorithm depends on the input database, we evaluate it on a wide range of real datasets, showing that we can achieve the benefits of data-dependence on both "easy" and "hard" databases.