In a database system, disclosure of confidential private data may occur if users can put together the answers of past queries. Traditional access control mechanisms cannot guard against such breaches to private data. Online auditing techniques have been advanced to limit such disclosure of private data. Essentially, before answering any query, these techniques inspect the answers of the past queries to determine whether answering this query would compromise the stated data disclosure policies. While the primary requirement for online auditing is high efficiency, existing auditing approaches are expensive with respect to both computational time and space. Specifically, this cost is excessive in the general case of auditing arbitrary aggregate queries over real-valued confidential attributes with respect to intervalbased privacy disclosure. In this paper, we model this problem as the well-studied linear programming (LP) problem and propose an efficient online auditing solution for const...