#### 3.4 Rising

Rising an n-dimensional cube is an operation that “lifts” the datacube to a higher dimension.
This can occur in two important applications. (1) Two datacubes having the same number of
dimensions and having the same dimensions can be merged together. Figure 8 displays an
example.

Figure 8: Rising Identical Cubes

This case is especially interesting for comparative studies of two or several datacubes,
comparing scenarios and outcoming of the same datacube. In LPL this is implemented as
Multiple Snapshot Analysis. Rising implies to introduce an additional dimension into the
resulting datacube. LPL automatically adds a set called _SNAP_. Hence the resulting datacube
has then n + 1. dimensions.

(2) The second important application arises when the actual cube has to be partitioned into
several groups, for example, along a time dimension, the months, one has to group the
dimension along quarters; or along a product dimension, one has to group them into various
product categories, etc (see Figure 9).

Figure 9: Rising Cubes by
Extending and Merging Dimensions

The original cube is partitioned into the desired parts and build from each part a complete
datacube of the original size – by getting eventually a very sparse cube. Then these cubes are
risen by “merging” them along a new dimension, which implements the partition, see Figure
10.

Figure 10: Rising Cubes by Extending and Merging
Dimensions

The idea behind this partition of a cube is that certain dimensions can be structured into
hierarchies (Year – Month – Week – Day, Continent – Country – Region – State). The partition
can be arbitrarily however, it can be even on several dimensions, that is, certain tuples of the
cube may belong to one part and other tuples to another part. The two most important
applications of this operation are grouping and hierarchy building in OLAP tool and grouping
and subgrouping in reports.