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Implications for the Cube Dependence Graph
When the homogeneity condition is dropped, the correctness of a rollup operation
does not follow from the cube dependence graph. The problem can be easily
realized by noting that the cube dependence graph of a single dimension corresponds
to its hierarchy schema. The anomalous behavior of the cube dependence
graph has deep implications for OLAP query processing, since the cube dependence
graph is used in algorithms to compute and maintain data cubes (Mumick,
Quass, & Mumick, 1997), and to speed up OLAP query processing (Harinarayan
et al., 1996).
Implications for Relational OLAP Models
Kimball (1996) argues that the best logical model to place OLAP queries is the
star schema. In the star schema the dimension consists of a single table where the
categories are arranged as attributes. We will refer to this table as a star dimension.
The table organizes the dimension elements as tuples, and allows simple
tuple browsing to place filters in OLAP queries. A star dimension requires the
hierarchy schema to have a single bottom category, which is the key attribute of
the table. The edges in the hierarchy schema are regarded as functional dependencies
over the table.
Another relational realization of OLAP data is the snowflake schema, which yields
snowflake dimensions.
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