Therefore, one can use the functional (and inclusion) dependencies in order to replace
grouping attributes. In a similar manner functional and inclusion dependencies
2 Karayannidis, Tsois, & Sellis
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allow the modification of join conditions, as explained in detail by Tsois (2005) and
Tsois and Sellis (2003). By replacing grouping attributes and join conditions, the
hierarchical pregrouping technique can group the fact table tuples very efficiently
before the residual join operations, it can push join operations above the grouping
operations and it can even remove completely some of the join operations.
The key idea used in the hierarchical pregrouping transformation is the following:
if a hierarchical attribute hk of a dimension Di is used in the query evaluation
plan just for grouping or just for an equi-join operation, then this attribute can be
replaced by its encoded form which exists within (as a prefix) the corresponding
h-surrogate. If hski is the corresponding h-surrogate, the encoded value of hk is
denoted as hski:hk.
For example, for the LOCATION dimension in our running example of Figure 4,
we can use the prefix part of the h-surrogate to group on the Area attribute, instead
of using the actual Area attribute.
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