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

4.3 Cost-Based Vectorization
scheme has a linear time complexity of O(m). As a result, the overall complexity of the
exhaustive computation is still dominated by the enumeration of candidate distribution
schemes, and hence, it has an exponential time complexity of O(2 m ).
Heuristic Computation Approach
Due to this exponential complexity of the P-CPV, a search space reduction approach for
determining the (near) cost-optimal solution for the P-CPV is required. Therefore, we
present a heuristic algorithm that solves the P-CPV and the Constrained P-CPV with
linear complexity of O(m). The core idea is to use a first fit (next fit) approach of merging
operators into execution buckets until the maximum constraint is reached.
Algorithm 4.3 Cost-Based Plan Vectorization (A-CPV)
Require: operator sequence o
1: A ← ∅, B ← ∅, k ← 0
2: max ← max m i=1 W (P ′ , o i ) + λ
3: for i ← 1 to |o| do // for each operator o i
4: if o i ∈ A then
5: continue 3
6: k ← k + 1
7: b k (o i ) ← create bucket over o i
8: for j
(
← i + 1 to |o| do // for each following operator o j
∑|bk
)
|
9: if c=1 W (o c) + W (o j ) ≤ max then
10: b k ← add o j to b k
11: A ← A ∪ o j
12: else
13: break 9
14: B ← B ∪ b k
15: return B
Algorithm 4.3 illustrates the concept of the cost-based plan vectorization algorithm.
The operator sequence o is required. First, we initialize two sets A and B as empty sets.
Thereafter, we compute the maximal costs of a bucket max with max = max m i=1 W (o i)+λ
followed by the main loop over all operators. If the operator o i belongs to A (operators
already assigned to buckets), we can proceed with the next operator. Otherwise, we
create a new bucket b k and increment the number of buckets k accordingly. After that, we
execute the inner loop in order to assign operators to this bucket such that the constraint
∑ |bk |
c=1 W (o c) ≤ max holds. This is done by adding o j to b k and to A. Here, we can ensure
that each created bucket has at least one operator assigned. Finally, each new bucket b k
is added to the set of buckets B.
The heuristic character is reasoned by merging subsequent operators. This is similar to
the first-fit (next fit) algorithm [Joh74] of the bin packing problem but with the difference
that the order of operators must be preserved. Thus, there are cases, where we do not find
the optimal scheme. However, this algorithm often leads to good or near-optimal results.
In conclusion, we use this heuristic as default computation approach, which motivates a
more detailed complexity and cost analysis, which we discuss in the following.
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