Applying OLAP Pre-Aggregation Techniques to ... - Jacobs University

70 4. Answering Basic Aggregate Queries Using Pre-Aggregated Data
Cost of aggregating sub-partitions of the closest dominant pre-aggregate
The cost C agg can be calculated as follows:
|SP |
∑
C agg (p cd ) = C dec (p cd ) + C r (s i ), (4.12)
where C dec is the cost of decomposing p cd into a set SP of sub-partitions, and C r is the
cost of aggregating each resulting sub-partition s ∈ SP from raw data.
4.3 Implementation
This section describes the application of a query optimization technique that transforms
an input query written in terms of arrays so that it can be executed faster using
pre-aggregated data. The query processing module of an array database management
system (RasDaMan) has been extended with our pre-aggregation framework for query
rewriting, and has been implemented as part of the optimization and evaluation phases.
As discussed earlier in this chapter, there are two problems related to the computation
of an aggregate query using pre-aggregated data. First, we must find all pre-aggregates
that can be used to compute an aggregate query, including those that provide partial
answers. Next, from all candidate pre-aggregates, we must find the one that minimizes
the execution time (or cost) for computing the query. Our solution is based on an existing
approach for answering queries using views in OLAP applications. Halevy et
al. [95] showed that all possible rewritings of a query can be obtained by considering
containment mappings from the bodies of the views to the body of the query. They
also showed that such characterization is a NP-complete problem.
The QUERYCOMPUTATION procedure returns the result of a query or an execution
plan for a given query Q. An execution plan is an indicator of the kind of data that
must be used to compute the query. It returns a raw indicator if the query must be
computed from the original data. Other valid indicators include IP AS, OP AS, and
DP AS, which indicate that the query will be answered using one or more partial
pre-aggregates.
The input of the algorithm is a query tree Q t of an aggregate query. The algorithm
first verifies if the conditions for a PERFECT-MATCHING between the query and the
pre-aggregated queries are satisfied. If a perfect-matching is found, it returns the result
of the pre-aggregated query. Otherwise, the algorithm verifies if the conditions for a
PARTIALMATCHING between the query and set of pre-aggregate queries are satisfied.
Then, the algorithm makes use of our cost model to determine the cost of using preaggregates
that satisfy partial-matching conditions for the computation of the query,
and the cost of computing the query using the original data. Finally, the algorithm
picks the plan with least cost in terms of execution time. The algorithm makes use of
the following auxiliary procedures:
• DECOMPOSEQUERY(Q t ) examines the nodes of the query tree Q t and generates
a standardized representation S qt that can be manipulated via SQL statements.
i=0