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

6 On-Demand Re-Optimization
6.3.1 Optimization Algorithm
Recall our search space shown in Figure 6.3. If certain optimality conditions are violated,
we apply directed re-optimization according to those violations. At this point, we know
the violated optimality conditions and the optimization techniques, which produced these
conditions. For directed re-optimization, we additionally need to determine the minimal
set of operators that should be reconsidered by those techniques. In this context, the
transitivity property of the PlanOptTree must be taken into account.
Example 6.6 (Determining Re-Optimization Search Space). Assume the PlanOptTree
of our example. During initial optimization, selectivities of sel(o 2 ) = 0.2, sel(o 3 ) = 0.3
and sel(o 4 ) = 0.4 resulted in the optimality conditions shown in Figure 6.7(a).
o 2 o 3
o 4
o 2 o 3
o 4
|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(o2)
sel(o3)
sel(o4)
sel(o2)
sel(o3)
sel(o4)
≤
≤
≤
≤
(a) Initiating (Violated) OCNode
(b) Transitive OCNode
Figure 6.7: Determining Re-Optimization Potential
Re-optimization was triggered because the selectivity of operator o 2 changed to sel(o 2 ) =
0.45. Thus, we need to reconsider operators o 2 and o 3 during re-optimization. However,
due to the transitivity of optimality conditions, we evaluate operator o 4 as well, because we
do not know in advance if the implicit optimality condition of sel(o 2 ) ≤ sel(o 4 ) still holds.
The PlanOptTree is traversed as shown in Figure 6.7(b) to determine that this transitive
condition is violated as well.
From a macroscopic view, we follow a bottom-up approach from the optimality conditions
to determine all operators for directed re-optimization. We start at each violated
optimality condition and traverse (without cycles) all other optimality conditions that
are reachable over transitivity connections. Such a transitivity connection is defined as
an atomic or complex statistic node connected with two or more optimality conditions.
Transitivity chains of arbitrary length are possible, where the end is given by the lack of
transitive connections or by the first condition that is still optimal.
Algorithm 6.3 illustrates how to trigger re-optimization. During statistics maintenance,
all violated optimality conditions are added to the set OC. When triggering reoptimization,
we traverse the logical transitivity chains for each optimality condition in
OC. For the left operator of the optimality condition, we check the transitivity filter (direction
of condition operands and its comparison operator) (line 4). If it holds, we check
the transitive optimality filter for this reachable optimality condition (line 5). If optimality
is violated, we mark this OCNode as a transitively violated condition, add it to OC
(line 6) and proceed recursively along the left chain (line 7). This is done similarly for the
right operator of the optimality condition (lines 8-12). Finally, we invoke the optimizer
with the set OC. The optimizer uses the violated optimality conditions and all involved
operators (line 13). Despite the unidirectional references of strata 1 and 2, we can efficiently
determine these operators. After successful re-optimization, the PlanOptTree is
178