Implementing Operations to Navigate Semantic Star Schemas

Alberto Abelló, José Samos and Fèlix SaltorU. Politècnica de Catalunya & U. de Granada

November 7th, 2003

DOLAP

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Contents

Related Work Multidimensional Algebra Translation to SQL New Drill-across possibilities Conclusions

Con

tent

s

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Example of Multi-star Schema

Rel

ated

wor

k

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Multi-star Schemas Kimball: Share Dimensions Giovinazzo: Galaxy sharing Dimensions Pedersen and Jensen: Multidimensional

Object Family sharing subdimensions Gopalkrishnan, Li, and Karlapalem: Multi-

star Schemas normalizing fact tables Moody and Kortink:

– Constellation (hierarchically linked fact tables)– Galaxy (share Dimensions)– Star Cluster (sharing subDimensions)

Rel

ated

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Semantic Relationships

Tryfona, Busborg, and Christiansen: EER Trujillo, Palomar, Gómez and Song: UML

(Generalization and Association inside a Star)

Abelló, Samos and Saltor: UML (Generalization, Association, Derivation and Flow between Stars)

Rel

ated

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k

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Cube M

ulti

dim

ensi

onal

Alg

ebra

A Cube is and injective function from an n-dimensional finite space (defined by the cartesian product of n functionally independent Levels {L1,..,Ln}), to the set of instances of a Cell (Cc).

c:L1 x .. x Ln Cc injective

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Composition of functions M

ulti

dim

ensi

onal

Alg

ebra

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Primitive Operations M

ulti

dim

ensi

onal

Alg

ebra

Drill-across Change Base Roll-up Union Dice Projection

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Operations (I) M

ulti

dim

ensi

onal

Alg

ebra

Change Base :Lo

1 x .. x Lon Li

1 x .. x Lim injective

:Cic Co

c injective

Drill-across

co(x) = (ci) = (ci(x))

co(x) = (ci) = ci( (x))

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Operations (II) M

ulti

dim

ensi

onal

Alg

ebra

Union

Roll-up

co(x) = c1 c2 =

:Lij Lo

k exhaustive

co(x) = (ci) = ci(y)(y) = x

{c1(x) if xDom(c1)c2(x) if xDom(c2)

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Operations (III)

Dice

co(x) = m1,..,mk(ci) = ci(x)[m1,..,mk]

Projection

co(x) = P(ci) ={ci(x) if P(x)undef if ¬P(x)

Mul

tidi

men

sion

al A

lgeb

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Derived Operations: Slice

co(x) = sliceLi=k(ci) = L1x..xLi-1xLi+1x..xLn( Li=k

(ci))

Mul

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men

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Basic query T

rans

lati

on to

SQ

L

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Dice T

rans

lati

on to

SQ

L

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Roll-up T

rans

lati

on to

SQ

L

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Change Base T

rans

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on to

SQ

L

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Drill-across T

rans

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on to

SQ

L

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Projection T

rans

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on to

SQ

L

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Union T

rans

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on to

SQ

L

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Effects of operations T

rans

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on to

SQ

L

Clause ChangeBase Drill-across Dice Roll-up Projection Union

SELECT Level (replace)

Measure (add)

Level (replace)

Measure (remove)

FROM Dimension (add)

Fact (add)

WHERE links (add)

links (add)

AND OR

GROUP BY Level (replace)

Level (replace)

ORDER BY Level (replace)

Level (replace)

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UML RelationshipsN

ew D

rill

-acr

oss

Pos

sibi

liti

es

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DerivationN

ew D

rill

-acr

oss

Pos

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Implementation: Updatable views ChangeBase

– View to table -> OK– Table to view -> Iff view subsumes WHERE

Drill-across– View to table -> OK– Table to view -> Outer join

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GeneralizationN

ew D

rill

-acr

oss

Pos

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es

Implementation: One table for superclass and another one for each subclass

ChangeBase – Sub to super -> OK– Super to sub -> Iff criterion subsumes WHERE

Drill-across– Sub to super -> OK– Super to sub -> Outer join

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AssociationN

ew D

rill

-acr

oss

Pos

sibi

liti

es

Implementation: Foreign keys ChangeBase

– 1:1 -> OK– 1:N and N:1 -> Depends on the bases

Drill-across– 1:1 -> OK– 1:N -> Do it to an upper detail level being 1:1– N:1 -> Double counting– Zeros -> Outer join

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FlowN

ew D

rill

-acr

oss

Pos

sibi

liti

es

Implementation: Foreign keys ChangeBase

– #old=#new -> OK– #old<>#new -> Weighting factors for facts– Appear or disappear -> Dice apropriately

Drill-across– #old=#new -> OK– #old<>#new -> ChangeBase– Appear or disappear -> Outer join

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Conclusions

Navigational (algebraic) queries Smoothly implemented on SQL Multistar semantic queriesC

oncl

usio

ns

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Que

stio

ns