The vision of the OMG´s Model-Driven Architecture (MDA) has
necessitated the extensive research of model compilers, which are able to
process graph-based visual models specified mainly in the Unified Modeling
Language (UML). A possible mechanism for the realization of MDA model
compilers can be graph rewriting-based transformation approach. Previous work
has introduced the tool Visual Modeling and Transformation System, which uses
graph rewriting as transformation mechanism, but the pattern language of
the rewriting rules consists of UML class diagram elements instead of object
diagram level patterns. This paper provides the algorithmic background for the
application of these rules specified by the class diagram elements. To achieve
that, it examines the allowed instantiation configuration based on the UML
standard, and supplies a constructive algorithm to compute the allowed number
of the objects participating in a valid instantiation of a class model.
Furthermore, starting from the VF2 algorithm, the pattern matching algorithm
for the left hand side of the metamodel-based rewriting rule is provided via
several optimization steps examined