Physical Data Warehouse Design - Data Warehouse Systems: Design and Implementation - page 241

table has a quantity value equal to the maximum in the view so the maximum
value remains the same and the counter is increased to 7. The tuple for p4 in
the summary-delta table has a maximum value greater than the maximum
in the view, and thus, the view must be updated with the new maximum and
the new counter.
Now consider the deletions. The tuple for p5 in the summary-delta table
has a quantity value smaller than the maximum in the view so the view is not
modified. The tuple for p6 in the summary-delta table has a quantity value
equal to the maximum in the view but with a greater count value. In this
case, we decrease the counter in the view to 1. The tuple for p7 illustrates
why the MAX function is not self-maintainable with respect to deletions.
The maximum value and the counter in the summary-delta table are equal
to those value in the view. There are two possible cases. If there are other
tuples in the base table with the same combination ( p7 , t7 ), we must obtain
the new maximum value and the new count from the base tables. This case
is depicted in Fig. 7.5 c. Otherwise, if there are no other tuples in the base
table with the same combination ( p7 , t7 ), we must simply delete the tuple
from the view.
The algorithm for refreshing the view DailySalesMax from the summary-
delta table SD DailySalesMax is left as an exercise.

7.4 Computation of a Data Cube

In Chap. 5 , we have explained how the data cube could be computed by
means of an SQL query, where the all value is represented by the null value.
Computing the whole data cube in this way from the base fact and dimension
tables could become extremely hard unless an adequate strategy is applied.
The simplest method, consisting in performing the GROUP BY queries for
each view and then taking their UNION , would be unacceptable in real-life
applications. Thus, several optimization techniques have been proposed for
this. We study next some of them in order to convey the main idea.
The optimization methods start with the notion of data cube lattice .
In this lattice, each node represents a possible aggregation of the fact data,
where there is an edge from node i to node j if j can be computed from i and
the number of grouping attributes of i is the number of attributes of j plus
one. For instance, given an aggregate view by CustomerKey and ProductKey
of the Sales table of the previous section, we can compute the total sales
amount by customer directly from this view, without computing it from the
base table. In what follows, to avoid overloading figures, we will work with the
lattice depicted in Fig. 7.6 , corresponding to a four-dimensional data cube,
with dimensions A , B , C ,and D . In this lattice, an edge from ABC to AB means
that the summary table AB can be computed from ABC . We do not include
in the lattice the transitive edges, for example, edges like ABCD

→ AB .