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Extra resources for Algorithm for approximating complex polynomial zeros (1998)
Example text
As we explain in Sect. 5, the merging of two schemas is driven by a mapping that tells how elements of the two schemas, specifically the support elements of c , correspond to each other. The mapping between d1 and c is shown in Fig. 2 as an arc connecting the two enclosed rectangles. This mapping can be obtained by “composing” the existing mappings between c , c, s1 , s2 , d1 , and d1 as Invert(c c ) ∗ Invert(s2 c) ∗ Invert(s1 s2 ) ∗ s1 d1 ∗ d1 d1 . , the domains and ranges of the mappings need to be swapped.
For example, if an operator returns more than one argument (as does our implementation of the operator Match), some of which are not used subsequently (as in script PropagateChanges in Sect. 1), they can be tacitly ignored. For minimizing the amount of GUI programming needed for visualizing various kinds of models, we used the following technique. We require an operator like WriteSQLDDL to output not only the textual representation of the 44 3. Implementation and Applications model, but also a data structure that describes how the terms in the text relate to the model elements, or graph nodes.
Implementation and Applications a target node and x2 is a source node of map. Analogously, the edge z, z1 is tagged with o+, since z does not appear in map at all. If we knew that o+ edges are always preferred over +− edges, then, in a conflict x, z1 could be eliminated without asking the engineer. We examined a variety of merge problems in the context of relational schemas, XML schemas, and SQL views, and established empirically a total order among all tag variations, which helps resolve many conflicts automatically in a way that matches human intuition.