CONCLUSIONS

In this chapter, the issue of the characterization of a hierarchy is proposed. We distinguished between hierarchies in which the mapping between different levels is full and hierarchies in which this condition is not verified. Then, we defined the concepts of multiplicity of a given hierarchy and of multiple hierarchies.

Based on the definitions and concepts proposed in this paper, we discussed the characterization of the OLAP operators involved in the hierarchy manipulation. In particular, depending on the type of hierarchy, we studied the different behavior of the roll-up and the drill-down operators in order to keep consistent data that are the result of the queries. We also characterize the slice operator, defining the implicit dimension concept and specifying two different types of operator: P-slice and T-slice. Finally, we proposed an enlargement of the operator set, specifically for hierarchy manipulation, which are the Insert level, the Delete level, the Add multiplicity, and the Add level operators. For each situation discussed, clear examples are given.