Efficient Traversal in Data Warehouse Based on Concept Hierarchy Using Galois Connections

This paper propose a new methodology for efficient implementation of OLAP operations using concept hierarchies of attributes in a data warehouse. The different granularity associated with a particular dimension and the hierarchy amongst those may be represented as a lattice. The focus is to move up (roll-up) and down (drill-down) within the lattice structure using an algorithm with optimal time complexity. In this paper, a new algorithm has been proposed using a dynamic data structure that reduces over time resulting in better space utilization and also reduction of computation time. A Galois Connection is identified on this lattice structure with well-defined abstraction and concretization functions based on the concept hierarchy. The contribution offers formalism in analysis using concept hierarchy in an abstract interpretation framework.