Cost-Based Optimization of Integration Flows - Datenbanken ...

4.3 Cost-Based Vectorization
b i with i ∈ [1, k] according to the constrained optimization objective
⎛ ⎞
φ c = min
m
l k | ∀i ∈ [1, k] : ∑ bi
⎝ W (o j ) ⎠ ≤ W (o max ) + λ, (4.8)
k=1
where λ (with λ ≥ 0) is a user-defined absolute parameter to control the cost constraint.
There, λ = 0 leads to the highest meaningful degree of parallelism, while higher values of
λ lead to a decrease of parallelism.
Essentially, one can configure the absolute parameter λ in order to influence the number
of threads. The higher the value of λ, the more operators are assigned to single execution
buckets, and thus, the lower the number of buckets and the lower the number of required
threads. However, the decision on merging operators is still made in a cost-based manner.
Based on the defined cost-based vectorization problems, we now investigate the resulting
search space. Essentially, both problems exhibit the same search space because they only
differ in the optimization objective φ, where the worst-case time complexity depends on
the structure of a given plan. Figure 4.12 illustrates the best case and the worst case.
j=1
Fork o 1
o 1 o 2 o 3 o 4 o 5 o 6 o 7
o 2 o 3 o 4 o 5 o 6 o 7
(a) Best-Case Plan P b (b) Worst-Case Plan P w
Figure 4.12: Plan-Dependent Search Space
The best case from a computational complexity perspective is the sequence of operators
(see Figure 4.12(a)), where each operator has a data dependency to its predecessor. Here,
the order of operators must be preserved when assigning operators to execution buckets. In
contrast, the worst-case is a set of operators without any dependencies between operators
(see Figure 4.12(b)) because there, we could create arbitrary combinations of operators.
We use an example to illustrate the resulting plan search space for the best case.
Example 4.6 (Operator Distribution Across Buckets). Assume a plan P with a sequence
of four operators (m = 4). Table 4.2 shows the possible plans for the different numbers of
buckets k.
Table 4.2: Example Operator Distribution
|b| b 1 b 2 b 3 b 4
Plan 1 k = 1 o 1 , o 2 , o 3 , o 4 - - -
Plan 2 k = 2 o 1 o 2 , o 3 , o 4 - -
Plan 3 o 1 , o 2 o 3 , o 4 - -
Plan 4 o 1 , o 2 , o 3 o 4 - -
Plan 5 k = 3 o 1 o 2 o 3 , o 4 -
Plan 6 o 1 o 2 , o 3 o 4 -
Plan 7 o 1 , o 2 o 3 o 4 -
Plan 8 k = 4 o 1 o 2 o 3 o 4
We can distinguish eight different (2 4−1 = 8) plans, where Plan 1 is the special case of an
instance-based plan and Plan 8 is the special case of a fully vectorized plan.
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