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

3.2 Prerequisites for Cost-Based Optimization
• Comparability of Control- and Data-Flow-Oriented Operators: The double-metric
cost model enables the comparison of data-flow and control-flow-oriented operators
by their normalized execution time. In contrast to empirical cost models, the double
metric cost model includes interaction- and control-flow-oriented operators as well.
• Plan Cost Monotonicity: The Picasso project [RH05] has shown that the assumption
of Plan Cost Monotonicity (PCM) holds for most queries in commercial DBMS even
over all plans of a plan diagram [HDH07]. In contrast, this assumption always holds
for our cost model of integration flows with regard to a single plan. As a result,
the costs of a plan are monotonically non-decreasing with regard to any increasing
influencing parameter such as selectivities, cardinalities, or execution times.
• Asymmetric Cost Functions: The cost model exhibits asymmetric cost functions,
i.e., the ordering of binary operator inputs has influence on the computed costs.
Thus, commutativity of inputs must be considered during optimization.
• No ASI Property: Finally, the cost model does not exhibit the ASI (Adjacent Sequence
Interchange) property [Moe09]. This property is given if and only if there is
a ranking function of data sets such that the ordering of ranks is the optimal join
ordering. Due to (1) possibly correlated external data sets and (2) different join
implementations including the merge-join (which is known to not having the ASI
property [Moe09]) our cost model does not exhibit this property.
Cost Estimation
In the following, we illustrate the cost estimation, using the known data-flow-oriented
optimization technique of eager group-by [CS94] (type invariant group-by), as an example
rewriting technique.
Example 3.2 (Cost Estimation). Assume the plan P 3 with monitored execution statistics
and a plan P 3 ′ that has been created by rewriting P 3 during optimization (invariant groupby
due to N:1-relationship between data sets, e.g., given by message schema descriptions).
There are no statistics available for P 3 ′ . The plans are shown in Figure 3.4. The statistics
of subplans that are equivalent in P 3 and P 3 ′ can be reused. Thus, only the new output
cardinality |ds out (o ′ 5 )| and the execution times W (o′ 5 ) and W (o′ 4 ) have to be estimated.
Assuming a monitored join selectivity (where f is a shorthand for filter selectivity) of
f dsout(o 2 ),ds out(o 3 ) = |ds out(o 2 ) ⋊⋉ ds out (o 3 )|
|ds out (o 2 )| · |ds out (o 3 )| = |ds out (o 4 )|
|ds out (o 2 )| · |ds out (o 3 )| = 5,000
5,000,000 = 1
1,000
and a group-by selectivity of
f γdsout(o 4 ) = |γds out(o 4 )|
|ds out (o 4 )|
= |ds out(o 5 )|
|ds out (o 4 )| = 1,000
5,000 = 1 5 .
The selectivities are used in order to compute the output cardinalities of new or reordered
operators. Due to the invariant placement of the group-by operator, we can compute the
new group-by output cardinality and directly set the new join output cardinality by
| ˆds out (o ′ 5)| = f γdsout(o4 ) · |ds out (o 2 )| = 1 · 5,000 = 1,000
5
| ˆds out (o ′ 4)| = 1,000.
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