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Nesting Mappings: Basic Mapping
VLDB ‘06,September 12-15,2006 Author: Ariel Fuxman , Mauricio A. Hernandez , Howard Ho
Renee J. Miller, Paolo Papotti , Lucian Popa
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Mapping Scenario
Source Schema
Target Schema
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Basic Mapping
• Disadvantage:1.Inefficiency in execution.2.Redundancy in the specification.3.Underspecified grouping semantic.
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Nesting Mapping
• To handle the above issues , we proposed an extension to basic mappings based on arbitrary nesting of mapping formulas within other mapping formulas.
• We call this formalism nested mappings.
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Basic Mapping Algorithm
• Step 1:Computation tableaux.• Step 2:Generation of basic mapping.• Step 3:Pruning of basic mapping.
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Tableaux
• Each tableaux is primarily an encoding of one set type of a schema (for source schema and target schema).
• Tableaux include all related set types, that is,
set types must exist together according to the parent-child relationship in the schema.
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Computation of tableaux
• For each set type T ,we create primary path spells out the navigation path from root to elements of T.
• For each intermediate set ,there is a variable to denote elements of the intermediate set.
• Tableaux is obtained by primary path.
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Source and Target tableaux
• sdfasdf
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Generators
• We consider all the atomic type element that can be referred to from the variables in the tableaux for mapping purpose.
• We call the variables that appear in the tableaux generators.
• Ex:B3 includes dname, budget , ename , salary , pname , pid.
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Generation of basic mapping(1/2)
• Basic mappings are generated by pairing in all the possible ways the source and the target tableaux.
• For each pair(A,B) of tableaux , let V denote the set of elements that are covered by both tableau A and tableau B .
• For example: (A1,B1)=>dname. (A1,B4)=>dname ,pname.
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Generation of basic mapping(2/2)
• We write the basic represented by (A,B,V) as .
• Not all the possible (A,B,V) can generate actual mappings. We generate a basic mapping only if it is not subsumed and not implied by other basic mapping.
VBA .
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Subtableau
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Tableaux hierarchies
• For each schema , the subtableau relationship induces a directed acyclic graph of tableaux, with an edge from A to A’ whenever A<=A’
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Pruning of basic mapping
• The pruning step reduce the number of candidate mappings that the nesting algorithm will have to explore.
• We generate a basic mapping only if it is not subsumed and not implied by other basic mapping.
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Subsumed
• 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’
• By subsumption condition ,we don’t have to consider (A,B,V) since it’s covered by (A’,B’,V’)
• For example:
VBA .''.' VBA
}.{}.{ 1121 dBAbysubsumedisdBA
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Imply
• A basic mapping may be logically implied by another basic mapping.
• There is a simpler test suffices as follow:
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Nestable
• We call a basic mapping is nestable inside a basic mapping if the following holds:
(1) A2 ,B2 are strict subtableaux of A1 ,B1 ,respectively.
(2) V2 is a strict superset of V1.
(3) There is no correspondence v in V2-V1 whose target elements are covered by B1
222 .VBA
111 .VBA
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Nestable (Example)
(1) A2 ,B3 are strict subtableaux of A1 ,B4 ,respectively.
(2) {d,p,e,s} is a strict superset of {d,p}.(3) There is no correspondence v in V2-V1 whose target elements are covered by B4
},,,{.322 sepdBAm },{.411 pdBAm Nestable inside