Equivalence of OLAP Dimension Schemas

Dimension schemas are abstract models of the data hierarchies that populate OLAP warehouses. Although there is abundant work on schema equivalence in a variety of data models, these works do not cover dimension schemas. In this paper we propose a notion of equivalence that allows to compare dimension schemas with respect to their information capacity. The proposed notion is intended to capture dimension schema equivalence in the context of OLAP schema restructuring. We offer characterizations of schema equivalence in terms of graph and schema isomorphisms, and present algorithms for testing it in well known classes of OLAP dimension schemas. Our results also permit to compare the expressiveness of different known classes of dimension schemas.