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

3 Fundamentals of Optimizing Integration Flows
purpose, the path probabilities P (path i ) (as relative frequencies over the sliding window)
and the absolute costs for evaluation of a path expression W (expr pathi ) are needed in order
to compute the relative costs for accessing a Switch path with W (expr pathi )/P (path i ).
As the core concept of WD1, we reorder Switch path expressions according to their
relative costs for expression evaluation. When applying this technique we need to ensure
the semantic correctness, where the structure of an expression is assumed to be a set of
predicates attribute θ value. We define that only independent expressions (e.g., annotated
within the flow specification) can be reordered, while conditional expressions prevent any
reordering. This reordering of Switch paths is optimal (in the average case) if Switch
paths are sorted in ascending order of their relative costs, such that the following optimality
condition holds:
W (expr pathi )
P (path i )
With such a reordering, an execution time reduction of
≤ W ( )
expr pathi+1
. (3.19)
P (path i+1 )
∆W (path i , path i+1 ) = P (path i ) · W ( expr pathi+1
)
− P (pathi+1 ) · W (expr pathi ) (3.20)
is possible when reordering two paths path i+1 and path i .
In contrast to the reordering of independent expressions, for any expressions that refer
to the same attribute, the technique WD2 can be applied. There, the concept is to
merge expressions with equivalent attribute to a compound switch path in order to extract
the single value only once and to evaluate it multiple times. With such a merged path
evaluation, an execution time reduction of
∆W (path i , path i+1 ) = P (path i+1 ) · W ( )
expr pathi+1 (3.21)
can be achieved. The compound path can be reordered similar to normal Switch paths.
In consequence, the technique WD2 should be applied before WD1.
The following rewriting algorithm applies the reordering and merging of Switch paths.
First, we partition the expressions, according to the attributes (e.g., represented by
XPath expressions). If a partition contains multiple paths, we apply the merging by
replacing the two paths with one compound path that writes the extracted attribute
value to an operator-local cache and evaluates it multiple times. Therefore, all subpaths
of the compound path are annotated as compound. Second, we compute the relative
costs W (expr pathi )/P (path i ) for each path and reorder the path according to the
given optimality condition. In total, this rewriting algorithm exhibits a complexity of
O(m 2 ) = O(m 2 + m · log m) due to partitioning and sorting of Switch paths. We use an
example to illustrate the resulting execution time when using these techniques.
Example 3.12 (Reordering and Merging Switch Paths). Recall our example plan P 1 that
is shown in Figure 3.15(a). Further, assume that the costs for accessing each of the two
Switch paths has been monitored as W (expr) = 30 ms. We analytically investigate the
influence of varying path probabilities P (A) ∈ [0, 1] with P (A) + P (B) = 1. Figure 3.15(b)
illustrates the influence of reordering the switch paths (assuming independent expressions,
e.g., A : var1 = x and B : var2 = y), where the costs are computed by P (A) · W (expr) +
(P (A) · W (expr) + P (B) · W (expr)) due to the ordered if-elseif semantic. Based on the
equivalence of costs for evaluating the expressions, we benefit from reordering if P (A) <
P (B). This means, for P (A) < 0.5, we reorder (A, B) to (B, A) and thus, achieve the
shown benefits. Furthermore, Figure 3.15(c) illustrates the influence of merging switch
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