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

6 On-Demand Re-Optimization
such that both directed re-optimization and full re-optimization results in the same plan.
Hence, Theorem 6.2 holds.
As a result of directed re-optimization, we minimized the re-optimization overhead for
large plans and for optimization techniques with a large search space.
6.3.2 Updating PlanOptTrees
Due to directed re-optimization, where we only consider a subset of all plan operators, we
need to incrementally update the existing PlanOptTree according to the rewritten plan.
The extension of the optimizer interface is based on returning partial PlanOptTrees.
Thus, after successful re-optimization, we incrementally update the PlanOptTree with
the partial PlanOptTrees of the newly created subplans. More precisely, the problem is
to update a given PlanOptTree that includes violated optimality conditions using a set of
given partial PlanOptTrees. The result of this update must be semantically equivalent to
a full creation from scratch (A-IPC).
We follow an approach called Partial PlanOptTree Replacement. We start bottom-up
from all violated optimality conditions and remove those OCNodes except for transitively
violated conditions because the new partial PlanOptTree is already aware of them. Subsequently,
we traverse up the tree and remove all nodes that do not refer to at least one child
any longer. As a result, we remove all nodes included in violated optimality conditions.
Finally, we can apply the merging of partial PlanOptTrees for all new subplans similar to
creating the initial PlanOptTree.
Example 6.7 (Partial PlanOptTree Replacement). In Example 6.6, the optimality condition
sel(o 2 ) ≤ sel(o 3 ) and the transitive condition sel(o 2 ) ≤ sel(o 4 ) were violated. The
triggered re-optimization returned the partial PlanOptTree shown in Figure 6.8(a).
o 4 o 2
o 2 o 3
o 4
o 2
o 3 o 4
o 2
|ds in1| |ds out1|
|ds in1| |ds out1|
|ds in1| |ds out1| |ds in1| |ds out1|
|ds in1| |ds out1|
|ds in1| |ds out1|
|ds in1| |ds out1| |ds in1| |ds out1|
|ds in1| |ds out1|
sel(o4)
sel(o2)
sel(o2)
sel(o3)
sel(o4)
sel(o2)
sel(o3)
sel(o4)
sel(o2)
≤
(a) New Partial POT
≤
≤
≤
(b) POT during Replacement
≤
(c) POT after Replacement
≤
Figure 6.8: Partial PlanOptTree Replacement
For an incremental update (Figure 6.8(b)), we remove the violated optimality condition
sel(o 2 ) ≤ sel(o 3 ), the selectivity sel(o 2 ), operator o 2 and its statistics but before deletion,
we copy the statistics to the new PlanOptTree. The additional arrows illustrate the traversal
paths. We then merge the new partial PlanOptTree with the remaining PlanOptTree.
Operator o 4 and all of its conditions are reused and the result is the PlanOptTree shown
in Figure 6.8(c) representing plan optimality according to the statistics from Example 6.6.
Algorithm 6.4 illustrates the details of the incremental update approach. For each
optimality condition in the set of violated optimality conditions, we remove the OCNode
and reachable statistic nodes without children (lines 2-7). Then, we clear strata 1-2
180