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By Cruz F. R., Mateus G. R., Smith J. M.

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2 Morphisms Many metadata-intensive applications, such as data integration and warehousing tools, use a graphical metaphor like the one shown in Fig. 1 for representing schema mappings. These mappings are shown to the engineer as sets of lines connecting the elements of two schemas. We call such mappings (schema) morphisms. , a set of pairs l, r drawn from OID×OID. Clearly, a morphism is a weaker representation of a transformation between two models than an SQL view or the mapping languages and expressions suggested in (Bergamaschi et al.

26 2. Conceptual Structures and Operators Table type column:1 Copy ( a1 column:2 name PRODUCTS Column type a2 type SQLtype int name PID SQLtype varchar name PName a3 keyCol a4 type Table , a1 a2 a3 a4 )= type column:1 Column type a6 a5 name column:2 PRODUCTS type int name PID SQLtype varchar name PName a7 keyCol PrimaryKey SQLtype a8 type PrimaryKey Fig. 8. Examples of copying the model of Fig. 2. Similarly, RestrictRange is specified in terms of the operator RestrictDomain by first inverting the input morphism, then applying RestrictDomain, and finally inverting the resulting morphism once again.

The output model m satisfies the following properties: i. m contains all selected nodes, ii. 3 Operators 27 iii. , m can represent all information of m , and iv. m is a ‘minimal’ model that satisfies (i)-(iii). Condition (iii) can be characterized formally in terms of dominance and information capacity as suggested in (Hull 1986; Miller et al. 1994). , each model element of m has at most one counterpart in m . In general, a model may contain implicit information, such as transitive relationships between model elements.

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A Branch-and-Bound Algorithm to Solve a Multi-level Network Optimization Problem by Cruz F. R., Mateus G. R., Smith J. M.


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