Title: Privacy and the Complexity of Simple Queries
Description: As both the scope and scale of data collection increases, an increasingly large amount of sensitive personal information is being analyzed. In this thesis, we study the feasibility of effectively carrying out such analyses while respecting the privacy concerns of all parties involved. In particular, we consider algorithms that satisfy differential privacy (Dwork, McSherry, Nissim, and Smith, 2006), a stringent notion of privacy that guarantees no individual's data has a significant influence on the information released about the database. Over the past decade, there has been tremendous progress in understanding when accurate data analysis is compatible with differential privacy, with both elegant algorithms and striking impossibility results. However, if we ask further when accurate and computationally efficient data analysis is compatible with differential privacy then our understanding lags far behind. In this thesis, we make several contributions to understanding the complexity of differentially private data analysis: