Step-3: Classification of Aggregation Functions

• How hard to compute aggregate from sub-aggregates?

• Three classes of aggregates:

• Distributive
  • Compute aggregate directly from sub-aggregates
  • Examples: MIN, MAX ,COUNT, SUM

• Algebraic
  • Compute aggregate from constant-sized summary of subgroup
  • Examples: STDDEV, AVERAGE
  • For AVERAGE, summary data for each group is SUM, COUNT

• Holistic
  • Require unbounded amount of information about each subgroup
  • Examples: MEDIAN, COUNT DISTINCT
  • Usually impractical for a data warehouses!

We see that calculating aggregates from aggregates is desirable, but is not possible for non-additive facts.  So we deal with three types of aggregates i.e. distributive that are additive in nature, and then algebraic which are non-additive in nature. Therefore, such aggregates have to be computed from summary of subgroups to avoid the problem of incorrect results. The of course are the holistic aggregates that give a complete picture of the data, such as median, or distinct values. However, such aggregates are not desirable for a data warehouse environment, as it requires a complete scanning, which is highly undesirable as it consumes lot of time.

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