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

6.2 Plan Optimality Trees
We execute a full optimization only once during the initial deployment of an integration
flow. The optimizer contract is changed in a way that it returns the set of optimality
conditions. Thus, the resulting research challenge is how to organize these optimality conditions
for efficient statistic monitoring, condition evaluation, and directed re-optimization.
In contrast to existing passive structures such as matrix views [BMM + 04] that are used
and maintained by the re-optimizer for selective operators, we propose an active structure,
the so-called Plan Optimality Tree (PlanOptTree), which is a data structure that models
optimality of a plan. It indexes operators and their related statistics, which are included
in optimality conditions. As a result, we maintain only required statistics and we can
continuously evaluate optimality conditions. Re-optimization is actively triggered only if
necessary—in this case, it is guaranteed that we will find a plan with lower costs. Here,
directed re-optimization is applied only for operators included in any violated conditions.
Example 6.3 (PlanOptTree POT(P 5 )). Figure 6.4 shows the PlanOptTree of plan P 5 .
o 2 o 3
|ds in1| |ds out1| |ds in1| |ds out1|
sel(o 2) sel(o 3)
o 4
|ds in1| |ds out1|
sel(o 4)
o 6 o 5 o 7
W W W
W(expr A)
P(A)
W(expr B)
P(B)
≤
≤
(oc1) (oc2) (oc4)
Figure 6.4: PlanOptTree of Plan P 5
It includes two optimality conditions (oc 1 , oc 2 ) for expressing the order of the Selection
operators o 2 , o 3 and o 4 (see Figure 6.3(c)) according to their selectivities (oc 3 of Example
6.1 is omitted due to transitivity of conditions) and one condition (oc 4 ) regarding
branch prediction of the Switch 19 operator o 5 according to the weighted path probabilities.
In the rest of this chapter, we explain in detail how to create, update, and use these
PlanOptTrees in order to enable the vision of on-demand re-optimization.
≤
6.2 Plan Optimality Trees
In this section, we formally define the PlanOptTree and show how to create a PlanOptTree
for a given plan during the initial optimization of an integration flow. Further, we explain
how to use it for statistic maintenance and when to trigger re-optimization.
6.2.1 Formal Foundation
A PlanOptTree, which general structure is shown in Figure 6.5, models optimality conditions
of a plan and it is defined as follows:
Definition 6.1 (PlanOptTree). Let P denote the optimal plan with regard to the current
statistics. Further, let m denote the number of operators and let s denote the maximum
number of statistic types per operator. Then, the PlanOptTree is defined as a graph of
five strata representing all optimality conditions of P :
19 For the Switch operator multiple versions of statistics are monitored. This includes the total execution
time W (o i) as well as the different execution times of all expression evaluations W (expr i).
171