SEKE 2012 Proceedings - Knowledge Systems Institute

Fig. 1.
The ecommerce object model.
of defining metrics for OR mapping impacts on non-functional
characteristics. It has been shown that efficiency, maintainability,
and usability, among the set of all quality attributes
defined by the ISO/IEC 9126-1 standard, are characteristics
significantly influenced by OR mappings [8]. For each of those
attributes, we use a set of metrics suggested by Holder et
al. [8] and Baroni et al. [2]. The metrics are Table Access for
Type Identification (TATI), Number of Corresponding Table
(NCT), Number of Corresponding Relational Fields (NCRF),
Additional Null Value (ANV), Number of Involved Classes
(NIC) and Referential Integrity Metric (RIM).
To measure these metrics, we developed a set of queries to
execute over synthesized alternatives. For brevity, and because
it suffices to make our point, we concisely describe one of
these metrics and the corresponding query in the following.
Spacemaker supports the others as well.
The Number of Corresponding Relational Fields (NCRF)
metric specifies the extent of change propagation for a given
OR mapping. Specifically, the NCRF metric manifests the
effort required to adapt a relational schema after applying a
change, such as inserting or deleting an attribute, over a class.
According to the definition, given a class C, NCRF(C) specifies
the number of relational fields in all tables that correspond to
each non-inherited, non-key attribute of C. The specification
of a query we designated to measure the NCRF metric over
synthesized alternatives is given below:
NCRF(C) = #(C.attrSet - C.id). fAssociate. fields
The Alloy dot operator denotes a relational join. While
attrSet specifies a set of non-inherited attributes of a class,
fAssociate is a relation from a table field to its associated class
attribute. The query expressions then, by using the Alloy set
cardinality operator (#), defines the NCRF metric.
Exploring, Evaluating and Choosing
The next step is to explore and prune the space of mapping
alternatives according to quality measures. Spacemaker partitions
the space of satisfactory mixed mapping specifications
into equivalence classes and selects at most a single candidate
from each equivalence class for presenting to the end-user.
To partition the space, Spacemaker evaluates each alternative
with respect to previously described relevant metrics. So
each equivalence class consists of all alternatives that exhibit
the same characteristics. Specifically, two alternatives a 1 and
a 2 are equivalent if value(a 1 , m i ) = value(a 2 , m i ) for all
metrics (m i ). Because equivalent alternatives all satisfy the
mapping constraints, it suffices to select one alternative in
each equivalence class to find a choice alternative. Given
that quality characteristics are usually conflicting, there is
generally no single optimum solution but there are several
pareto-optimal choices representing best trade-offs.
C. Model Splitting
As with many formal techniques, the complexity of constraint
satisfaction restricts the size of models that can actually
be analyzed [7]. Our approach also requires an explicit
representation of the set of all quality equivalence classes of
mapping alternatives, which in general grows exponentially in
the number of elements in a model.
To address these scalability problems, we split the object
model into sub-models. The key idea is that since for association
relationships with cardinality of many-to-many, there
is just one applicable mapping strategy, i.e. own association
table, we make use of such relations to split the object model
into sub-models.
We consider an object model as a graph, G objModel =<
V,E >, where nodes V represent classes, and there is an
edge < v i ,v j > joining two nodes v i and v j if there is
a direct relationship including association and generalization
link between them. We assume that G objModel is connected.
Otherwise, we consider each sub-graph separately. An edge
joining two nodes v i and v j in a graph is a bridge if removing
the edge would cause v i and v j to lie in two separate subgraphs
[5]. A bridge is the only route between its endpoints. In
other words, bridges provide nodes with access to parts of the
graph that are inaccessible by other means. So, to decompose
a graph G objModel , we remove all bridges of type many-tomany
association.
To make our idea concrete we consider the ecommerce
domain model we adopted from Lau and Czarnecki [13].
According to the diagram shown in Figure 1, there are two
such bridges: < P roduct, Asset > and < Item, P roduct >.
By removing those bridges we obtain three smaller sub-graphs.
The gain then comes from the reduction in the sizes of
the constraint solving problems. That is, we replace a large
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