In this paper, an optimal aggregation and counter-aggregation (drill-down) methodology is proposed on multidimensional data cube. The main idea is to aggregate on smaller cuboids after partitioning those depending on the cardinality of the individual dimensions. Based on the operations to make these partitions, a Galois Connection is identified for formal analysis that allow to guarantee the soundness of optimizations of storage space and time complexity for the abstraction and concretization functions defined on the lattice structure. Our contribution can be seen as an application to OLAP operations on multidimensional data model in the Abstract Interpretation framework. © 2009 IEEE.