Convex cube: Towards a unified structure for multidimensional databases

In various approaches, data cubes are pre-computed in order to efficiently answer OLAP queries. Such cubes are also successfully used for multidimensional analysis of data streams. The notion of data cube has been explored in various ways: iceberg cubes, range cubes, differential cubes or emerging cubes. In this paper, we introduce the concept of convex cube which captures all the tuples satisfying a monotone and/or antimonotone constraint combination. It can be represented in a very compact way in order to optimize both computation time and required storage space. The convex cube is not an additional structure appended to the list of cube variants but we propose it as a unifying structure that we use to characterize, in a simple, sound and homogeneous way, the other quoted types of cubes.