Discrete algorithms and methods for security of statistical databases related to the work of Mirka Miller

This article gives a survey of discrete and combinatorial algorithms and methods for database security related to the work of Mirka Miller. The main contributions of Mirka Miller and coauthors to the security of statistical databases include the introduction of Static Audit Expert and theorems determining time complexity of its combinatorial algorithms, a polynomial time algorithm for deciding whether the maximum possible usability can be achieved in a statistical database with a special class of answerable statistics, NP-completeness of similar problems concerning several other types of statistical databases, sharp upper bounds on the number of compromise-free queries in certain categories of statistical databases, and analogous results on applications of Static Audit Expert for the prevention of relative compromise.