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# Basic Mapping

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### Basic Mapping

1. 1. Nesting Mappings: Basic Mapping<br />VLDB ‘06,September 12-15,2006<br /> Author: Ariel Fuxman , Mauricio A. Hernandez , Howard Ho<br /> Renee J. Miller, Paolo Papotti , Lucian Popa<br />1<br />
2. 2. Mapping Scenario<br />Source Schema<br />Target Schema<br />2<br />
3. 3. 3<br />
4. 4. 4<br />
5. 5. Basic Mapping<br />Disadvantage:1.Inefficiency in execution.2.Redundancy in the specification.3.Underspecified grouping semantic.<br />5<br />
6. 6. Nesting Mapping<br />To handle the above issues , we proposed an extension to basic mappings based on arbitrary nesting of mapping formulas within other mapping formulas.<br />We call this formalism nested mappings.<br />6<br />
7. 7. Basic Mapping Algorithm<br />Step 1:Computation tableaux.<br />Step 2:Generation of basic mapping.<br />Step 3:Pruning of basic mapping.<br />7<br />
8. 8. Tableaux<br />Each tableaux is primarily an encoding of one set type of a schema (for source schema and target schema).<br />Tableaux include all related set types, that is, set types must exist together according to the parent-child relationship in the schema.<br />8<br />
9. 9. Computation of tableaux<br />For each set type T ,we create primary path spells out the navigation path from root to elements of T.<br />For each intermediate set ,there is a variable to denote elements of the intermediate set.<br />Tableaux is obtained by primary path.<br />9<br />
10. 10. Source and Target tableaux<br />sdfasdf<br />10<br />
11. 11. Generators<br />We consider all the atomic type element that can be referred to from the variables in the tableaux for mapping purpose.<br />We call the variables that appear in the tableaux generators.<br />Ex:B3 includes dname, budget , ename , salary , pname , pid.<br />11<br />
12. 12. Generation of basic mapping(1/2)<br />Basic mappings are generated by pairing in all the possible ways the source and the target tableaux.<br />For each pair(A,B) of tableaux , let V denote the set of elements that are covered by both tableau A and tableau B .<br />For example: (A1,B1)=&gt;dname. (A1,B4)=&gt;dname ,pname.<br />12<br />
13. 13. Generation of basic mapping(2/2)<br />We write the basic represented by (A,B,V) as . <br />Not all the possible (A,B,V) can generate actual mappings. We generate a basic mapping only if it is not subsumed and not impliedby other basic mapping.<br />13<br />
14. 14. Subtableau<br />14<br />
15. 15. Tableaux hierarchies<br />For each schema , the subtableau relationship induces a directed acyclic graph of tableaux, with an edge from A to A’ whenever A&lt;=A’<br />15<br />
16. 16. Pruning of basic mapping<br />The pruning step reduce the number of candidate mappings that the nesting algorithm will have to explore.<br />We generate a basic mapping only if it is not subsumed and not impliedby other basic mapping.<br />16<br />
17. 17. Subsumed<br />A basic mapping is subsumed by a basic mapping ,if A,B are subtableaux of A’,B’ ,with at least one being strict , V = V’<br />By subsumption condition ,we don’t have to consider (A,B,V) since it’s covered by (A’,B’,V’)<br />For example: <br />17<br />
18. 18. Imply<br />A basic mapping may be logically implied by another basic mapping.<br />There is a simpler test suffices as follow:<br />18<br />
19. 19. Nestable<br />We call a basic mapping is nestable inside a basic mapping if the following holds:<br />A2 ,B2are strict subtableaux of A1 ,B1,respectively.<br />V2 is a strict superset of V1.<br />There is no correspondence v in V2-V1 whose target elements are covered by B1<br />19<br />
20. 20. Nestable (Example)<br />Nestable inside<br />A2 ,B3are strict subtableauxof A1 ,B4,respectively. <br />{d,p,e,s} is a strict superset of {d,p}.<br />There is no correspondence v in V2-V1 whose target elements are covered by B4<br />20<br />