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

5.2 Conceptual Framework 81
Benefit
The benefit of a candidate scale operation for pre-aggregation q, is computed by
adding the savings in query cost for each scaling operation in the workload dependent
on q, including all queries identical to q. That is, query q may contribute to
saving processing costs for the same or similar queries in the workload. In both cases,
specific matching conditions must be satisfied.
Full-Match Conditions. Let q be a candidate query for pre-aggregation and p a
query in workload Q. Let p and q both be scaling operations as defined in Eq. 5.1.
There is a full-match between q and p if and only if:
• the value of parameter objName[] in the scale function defined for q is the same
as in p
• the value of parameter ⃗s in the scale function defined for q is the same as in p
• the value of parameter resMeth in the scale function defined for q is the same
as in p
Partial-Match Conditions. Let q be a candidate query for pre-aggregation and p
be a query in the workload Q. There is a partial-match between p and q if and only if:
• the value of parameter objName[] in the scale function defined for q is the same
as in p
• the value of parameter resMeth in the scale function defined for q is the same
as in p
• the parameter ⃗s for both q and p is of the same dimensionality
• vector values defined in ⃗s for q are higher than those defined in p
Definition 5.5 (Benefit) – Let T ∈ Q be a subset of scaling operations that can
be fully or partially computed using query q. The benefit of query q per unit space,
denoted by B(q), is the sum of the computational cost savings gained by selecting
query q for pre-aggregation.
✷
B(q) = ((F (q) ∗ C(q)) + ∑ t∈T
(F (t) ∗ C r (t, q)))/size(q) (5.3)
where F (q) represents the frequency of query q in the workload, C ( q) is the cost of
computing query q on the original dataset, C r (t, q) is the relative cost of computing
query t from q, and size(q) is a function that returns the number of cells composing
the spatial domain component of a query q.