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

6 On-Demand Re-Optimization
stratum 1
stratum 2
stratum 3
RNode
o 1 o 2 o 3 o 7
ONode
nid=1 nid=2 nid=3 nid=7
stat 1 stat 3 stat 1 stat 3
stat 1 stat 1 stat 2 stat 5
SNode
monitored
statistics
stratum 4
cstat
cstat
cstat
CSNode
cstat
global memo
structure
stratum 5
ocond
ocond
OCNode
ocond
Figure 6.5: General Structure of a PlanOptTree
1. RNode: The single root node refers to m ′ with 1 ≤ m ′ ≤ m operator nodes (ONode).
2. ONode: An operator node is identified by a node identifier nid and refers to s ′ with
1 ≤ s ′ ≤ s statistic nodes (SNode), where s denotes the maximum number of atomic
statistic types.
3. SNode: A statistic node exhibits one of the s atomic statistic types, where a single
type must not occur multiple times for one operator o i . Further, each SNode contains
a list of statistic tuples monitored for o i , a single aggregate, as well as a reference to
a list of CSNodes and a list of OCNodes.
4. CSNode: A complex statistic node is a mathematical expression using all referenced
parent SNodes or CSNodes as operands, where a CSNode can refer to SNodes of
different operators. Further, it refers to a list of complex statistic nodes (CSNode)
and a list of optimality condition nodes (OCNode). Hence, arbitrary hierarchies
of complex statistics are possible. In addition, CSNodes can be used to represent
constant values or externally loaded values.
5. OCNode: An optimality condition node is defined as a boolean expression op 1 θ op 2 ,
where θ denotes an arbitrary binary comparison operator and the operands op 1 and
op 2 refer to any CSNode or SNode, respectively. The optimality condition is defined
as violated if the expression evaluates to false.
The nodes of strata 1 and 2 are reachable over unidirectional references, while nodes of
strata 3-5 are defined as bidirectional references (children and parents).
Although the PlanOptTree is a graph, we call it a tree, because from the viewpoint of
statistic maintenance, only the tree from strata 1 to 3 is relevant, while from the viewpoint
of directed optimization, each optimality condition is the root of a tree from strata 5 to
3. All references to children and parents are maintained as sorted lists ordered by their
identifier. Conceptually, known index structures can be used instead of lists. Furthermore,
each node of stratum 4 and stratum 5 is reachable over multiple paths. For this reason,
a PlanOptTree includes a MEMO structure in order to mark subgraphs that have already
been evaluated. Finally, we are able to exploit the following four fundamental properties:
• Minimal Monitoring: The PlanOptTree includes only operators and statistics that
are included in any optimality condition. Thus, we can easily determine the relevant
statistics for minimal statistics monitoring (given by stratum 2 and stratum 3).
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