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

104 6. Conclusion
query using pre-aggregated data is influenced by the structural characteristics of the
query and the pre-aggregate. Thus, by comparing query tree structures between the
two, one can determine if the pre-aggregated result contributes fully or partially to
the final answer of the query. The best case occurs when there is full-matching between
the query and the pre-aggregate, since the time taken to compute the query is
reduced to the time it takes to retrieve the result. However, in the case of partialmatching,
several pre-aggregates can be considered for computing the answer of a
query. The decision has to be made, therefore, as to which pre-aggregates provide the
best performance in terms of execution time. To this end, we distinguished between
different pre-aggregates and presented a cost-model to calculate the cost of using each
qualifying pre-aggregate. Then we presented an algorithm that selects the best execution
plan for evaluating a query considering pre-aggregated data. Tests performed on
real-life raster image datasets showed that our distinction between different types of
pre-aggregates is useful to determine the pre-aggregate providing the highest benefit
(in terms of execution time) for computing a given query.
We then described the issues of attempting to generalize our pre-aggregation framework
to support more complex aggregate operations, and justified our decision to focus
on one particular operation: scaling. Traditionally, 2D scaling operations have
been performed using image pyramids. Practice shows that pyramids are typically
constructed in scale levels of powers of 2, thus yielding scale vectors 2, 4, 6, 8, 16, 32, 64,
128, 256, and 512. The materialization of the pyramid requires an estimated 33% additional
storage space. Our pre-aggregation selection algorithm is similar to the pyramid
approach in that it selects a set of queries for materialization, where each level corresponds
to a scaling operation with a defined scale factor. However, the selection of
such queries is not restricted to a fixed number of levels interleveled by a power of two.
Instead, our selection algorithm considers the frequency of each query in the workload,
and how the results of each individual query can help to reduce the overall cost
of computing the workload. We compared the performance of our pre-aggregation algorithm
against that of image pyramids: results showed that for workloads with scale
vectors uniformly distributed our algorithm computes the workload 36% cheaper than
image pyramids, and requires 7% additional space than image pyramids. For scale
vectors following a Poisson distribution, our algorithm computes the workload at a
cost 55% cheaper than when using the pyramids approach. Further, our algorithm
can be applied to datasets of higher dimensions, a feature not supported by traditional
image pyramids.
6.1 Future Work
There are natural extensions to this work that would help expand and strengthen the
results. One area of further work is in adding self-management capabilities so that the
DBMS maintains statistics about each scaling operation appearing within the incoming
queries and, at some suitable time, adjust the pre-aggregate set accordingly. OLAP
dynamic pre-aggregation addresses a similar problem. Another area is in applying the
results studied here to the many real-world situations where data cubes contain one or