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Various methods for computing different measures in data cube construction are
discussed in depth in Chapter 5. Notice that most of the current data cube techno-
logy confines the measures of multidimensional databases to numeric data. However,
measures can also be applied to other kinds of data, such as spatial, multimedia, or
text data.

4.2.5 Typical OLAP Operations
“How are concept hierarchies useful in OLAP?” In the multidimensional model, data are
organized into multiple dimensions, and each dimension contains multiple levels of
abstraction defined by concept hierarchies. This organization provides users with the
flexibility to view data from different perspectives. A number of OLAP data cube opera-
tions exist to materialize these different views, allowing interactive querying and analysis
of the data at hand. Hence, OLAP provides a user-friendly environment for interactive
data analysis.

Example 4.4 OLAP operations. Let’s look at some typical OLAP operations for multidimensional
data. Each of the following operations described is illustrated in Figure 4.12. At the cen-
ter of the figure is a data cube for AllElectronics sales. The cube contains the dimensions
location, time, and item, where location is aggregated with respect to city values, time is
aggregated with respect to quarters, and item is aggregated with respect to item types.
To aid in our explanation, we refer to this cube as the central cube. The measure dis-
played is dollars sold (in thousands). (For improved readability, only some of the cubes’
cell values are shown.) The data examined are for the cities Chicago, New York, Toronto,
and Vancouver.
Roll-up: The roll-up operation (also called the drill-up operation by some vendors)
performs aggregation on a data cube, either by climbing up a concept hierarchy for
a dimension or by dimension reduction. Figure 4.12 shows the result of a roll-up
operation performed on the central cube by climbing up the concept hierarchy for
location given in Figure 4.9. This hierarchy was defined as the total order “street <
city < province or state < country.” The roll-up operation shown aggregates the data
by ascending the location hierarchy from the level of city to the level of country. In
other words, rather than grouping the data by city, the resulting cube groups the data
by country.
When roll-up is performed by dimension reduction, one or more dimensions are
removed from the given cube. For example, consider a sales data cube containing
only the location and time dimensions. Roll-up may be performed by removing, say,
the time dimension, resulting in an aggregation of the total sales by location, rather
than by location and by time.
Drill-down: Drill-down is the reverse of roll-up. It navigates from less detailed data
to more detailed data. Drill-down can be realized by either stepping down a concept
hierarchy for a dimension or introducing additional dimensions. Figure 4.12 shows the
result of a drill-down operation performed on the central cube by stepping down a