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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