Cardinality-based inference control in sum-only data cubes

Abstract

This paper addresses the inference problems in data warehouses and decision support systems such as on-line analytical processing (OLAP) systems. Even though OLAP systems restrict user accesses to predefined aggregations, inappropriate disclosure of sensitive attribute values may still occur. Based on a definition of non-compromiseability to mean that any member of a set of variables satisfying a given set of their aggregations can have more than one value, we derive sufficient conditions for non-compromiseability in sum-only data cubes. Under this definition, (1) the non-compromiseability of multi-dimensional aggregations can be reduced to that of one dimensional aggregations, (2) full or dense core cuboids are non-compromiseable, and (3) there is a tight lower bound for the cardinality of a core cuboid to remain non-compromiseable. Based on these results, taken together with a three-tier model for controlling inferences, we provide a divide-and-conquer algorithm that uniformly divides data sets into chunks and builds a data cube on each such chunk. The union of these data cubes are then used to provide users with inference-free OLAP queries.