Database Modeling and Design

172 CHAPTER 8 Business Intelligence
0.1
P = 0.9
0.1
0.9 0.1
0.9
0.1
0.9 0.1 0.9 0.1 0.9 0.1 0.9
0.001
0.009 0.009
0.081 0.009 0.081
0.081
0.729
a = 3 lefts
P 3 = 0.001
3
C = 1 bin
3
a = 2 lefts
P 2 = 0.009
3
C = 3 bins
2
a = 1 left
P 1 = 0.081
3
C = 3 bins
1
a = 0 lefts
P 0 = 0.729
3
C = 1 bin
0
Figure 8.15
Example of a binomial multifractal distribution tree
The values of P and k can be estimated based on sample data. The
algorithm used in [Faloutsos, Matias, and Silberschatz, 1996] has three
inputs: the number of rows in the sample, the frequency of the most
commonly occurring value, and the number of distinct aggregate rows
in the sample. The value of P is calculated based on the frequency of the
most commonly occurring value. They begin with:
k = ⎡Log 2 (Distinct rows in sample)⎤ 8.7
and then adjust k upwards, recalculating P until a good fit to the number
of distinct rows in the sample is found.
Other distribution models can be utilized to predict the size of a view
based on sample data. For example, the use of the Pareto distribution
model has been explored [Nadeau and Teorey, 2003]. Another possibility
is to find the best fit to the sample data for multiple distribution models,
calculate which model is most likely to produce the given sample data,
and then use that model to predict the number of rows for the full data
set. This would require calculation for each distribution model considered,
but should generally result in more accurate estimates.