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

4.3 Cost-Based Vectorization
where we determine the minimum costs only for the given k. Hence, the optimization
objective is to keep the maximum costs of execution buckets as low as possible. Due to
the explicitly given k, the constrained objective φ c is not applicable. Finally, the rewriting
algorithm can be reused as it is.
Heuristic Computation Approach
In contrast to the exhaustive computation, the heuristic approach requires major changes
when restricting k because we cannot exploit the maximum capacity of a bucket that
would result in any k and thus, would stand in conflict to the fixed k constraint. Hence,
we require an alternative heuristic to solve this optimization problem.
The heuristic algorithm (A-RCPV) for a restricted number of execution buckets k works
as follows. In a first step, we distribute the m operators uniformly across the given k
buckets, where the first m−k ·⌊m/k⌋ buckets get ⌈m/k⌉ operators and all other operators
get ⌊m/k⌋ operators assigned to them. In a second step, for each bucket, we check if the
performance can be improved by assigning its first operator to the previous bucket or its
last operator to the next bucket. There, the optimization objective φ (Equation 4.18)
is used to determine the influence in the sense of lower maximum bucket costs. Finally,
we do this for each operator until no more operators are exchanged during one run over
all operators. Due to the direct evaluation with φ, cycles are impossible and hence, the
algorithm terminates and it exhibits a linear time complexity of O(m). We illustrate this
using an example.
Example 4.8 (Heuristic Computation with Fixed k). Assume a fixed number of buckets,
k = 3. Figure 4.14 uses the plan and statistics from Example 4.7 and illustrates the
heuristic approach for fixed k.
given operator
sequence o
o1 o2 o3 o4 o5 o6
W(o1)=1 W(o2)=4 W(o3)=5 W(o4)=2 W(o5)=3 W(o6)=1
b1 b2 b3
k=3 o1 o2 o3 o4 o5 o6
max W(bi)=7
b1 b2 b3
o1 o2 o3 o4 o5 o6
max W(bi)=6
Figure 4.14: Heuristic Operator Distribution with Fixed k
We distribute the six operators uniformly across the three execution buckets. As already
mentioned, the performance of the plan depends on the most time-consuming bucket. In
our example, this is bucket 2, with W (b 2 ) = 7 ms. Now, we exchange operators. First, at
bucket 1, no operator is exchanged because transferring o 2 from b 1 to b 2 would increase the
maximum bucket costs. The same is true for a transfer of o 3 from b 2 to b 1 . However, we
can transfer o 4 from b 2 to b 3 and reduce the maximum costs to W (b 3 ) = 6 ms. Finally, we
require a final run over all buckets to check the termination condition.
As a result, one can solve both the P-CPV as well as the constrained P-CPV under
the restriction of a fixed number of execution buckets and thus, also with a fixed number
of threads. With this approach we can guarantee to overcome the problem of a possibly
large number of required threads.
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