Minimal Mappings (also on Wikipedia)
Given any two graph-like structures, e.g., database or XML schemas and ontologies, matching is usually identified as the problem of finding those nodes in the two structures which semantically correspond to one another. Any such pair of nodes is informally called a mapping.
Semantic matching has been proposed as a solution to the semantic heterogeneity problem at the level of schematic metadata (e.g., ontologies). Minimal mappings are high quality mappings such that i) all the other mappings can be computed from them in time linear in the size of the input graphs, and ii) none of them can be dropped without losing property i).
The proposed technique works on lightweight ontologies, namely on DAG-like graph structures where each node is labelled by a natural language sentence which can be used to compute the meaning of that node as a Description Logic (DL) formula, and where the formula associated to each node is subsumed by the formula of the node above. Furthermore we assume that each mapping is associated with one of the following semantic relations: disjointness, equivalence, more specific and less specific, as implemented for example by SMatch.
The main advantage of minimal mappings is that they are the minimal amount of information that needs to be dealt with. Notice that this is a rather important feature as the number of possible mappings can grow up to n*m with n and m the size of the two input ontologies. In particular, minimal mappings become crucial with large ontologies, e.g. DMOZ, where even relatively small subsets of the number of possible mappings, potentially millions of them, are unmanageable. Minimal mappings provide clear usability advantages. Many systems and corresponding interfaces, mostly graphical, have been provided for the management of mappings but all of them hardly scale with the increasing number of nodes, and the resulting visualizations are rather messy [1]. Furthermore, the maintenance of smaller sets of mappings makes the work of the user much easier, faster and less error prone. Look at [2] for a formal definition of minimal and, dually, redundant mappings, evidence of the fact that the set of minimal mappings always exists and it is unique and an algorithm for computing them.