Nested Data Cubes for OLAP

Abstract

We present a new model for OLAP, called the nested data cube (NDC) model. Nested data cubes are a generalization of other OLAP models such as f-tables [3], and hypercubes [2], but also of classical structures such as sets, bags, and relations. The model we propose adds to the revious models mainly flexibility in viewing the data, in that it allows for the assignment of priorities to the different dimensions of the multidimensional OLAP data. We also present an algebra in which all typical OLAP analysis and navigation operations can be formulated. We present a number of algebraic operators that work on nested data cubes and that preserve the functional dependency between the dimensional coordinates of the data cube and the factual data in it. These operations include nesting, unnesting, summary, roll-up, and aggregation operations. We show how these operations can be applied to sub-NDC’s at any depth, and also show that the NDC algebra can express the SPJR algebra [1] of the relational model. A major motivation for defining an algebra rather than a calculus, is that an algebra naturally leads to an implementation strategy. Importantly, we show that the NDC algebra primitives can be implemented by linear time algorithms.