## 5.1 Data Cube Computation: Preliminary Concepts

Data cubes facilitate the online analytical processing of multidimensional data. *“But how can we compute data cubes in advance, so that they are handy and readily available for query processing?”* This section contrasts full cube materialization (i.e., precomputation) versus various strategies for partial cube materialization. For completeness, we begin with a review of the basic terminology involving data cubes. We also introduce a cube cell notation that is useful for describing data cube computation methods.

### 5.1.1 Cube Materialization: Full Cube, Iceberg Cube, Closed Cube, and Cube Shell

Figure 5.1 shows a 3-D data cube for the dimensions *A*, *B*, and *C*, and an aggregate measure, *M*. Commonly used ...