Construction and Maintenance of Heterogeneous Data Warehouses - Data Warehousing Design and Advanced Engineering Applications - page 200

Figure 6. The two architectures of the DW of the example 12

W can be created according to two possible
different architectures (see Figure 6).

and are not all refreshed in the same way. Indeed,
given two setsA and B of integers: average ( A ∪ B ) ≠
average ( average ( A ), average ( B )) whereas max ( A ∪
B ) = max ( max ( A ), max ( B )).
In Palpanas, Sidle, Cochrane & Pirahesh, 2002;
Chou & Zhang, 2004, the aggregate functions have
been classified into three categories:

INCREMENTAL MAINTENANCE
OF DATA AND AGGREGATES

To help decision making, aggregates are computed
over DW. These aggregates can be calculated in
the same way using Ws architecture as well as
Wp. They are stocked in materialized views (MV)
called in some systemsAutomatic Summary Table
(AST). We discuss in this section different ways
to refresh these MV.
Updates realized on the source level are reflected
in the warehouse according to our ConstrView()
algorithm. This implies the update of the aggregates
in the view MV of this warehouse. Our maintenance
method consists in carrying out an incremental
update of MV. In the case of a flat architecture
(Wp), it is achieved by computing ΔWp resulting
from the sources updates. It is the same case for
star architecture Ws (compute delta update for
every fact and/or dimension which is affected by
the new update). To maintain MV we need to cal-
culate MV' on ΔWp. The new values of MV are
obtained by applying a full outer join operation
between MV and MV'. But before explaining our
incremental maintenance method, let us describe
the aggregate functions and their differences. The
aggregate functions belong to different categories

• distributive aggregate functions: a func-

tion f is distributive if for a group G, f ( G )
can be computed from f ( G s ) values where
G s are the G sub-groups. COUNT ALL ,
MAX , MIN and SUM are examples of
distributive functions.

• algebraic aggregate functions: a function f

is called algebraic if for a group G, f ( G ) can
be computed from a fixed number of inter-
mediate aggregates computed on G s sub-
groups. This extra data is usually stored in
auxiliary tables/views. AVG, VARIANCE
and STDDEV are examples of algebraic
functions.
and • holistic aggregate functions: the num-

ber of intermediate aggregates is unknown.
There is no known method to compute in-
crementally this kind of aggregates. The
only available solution remains in explor-
ing all data sources. This third class of
functions is not considered treated in this
work. COUNT DISTINCT and RANK
are examples of holistic functions.