Approximate Functional Dependencies for XML DataFabio Fassetti, Bettina Fazzinga

DEIS, University of Calabria, Italy

ADBIS 2007 - Varna (BUL), September 29 - October 3ADBIS 2007 - Varna (BUL), September 29 - October 3

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 2

Outline

Preliminaries Inference Problem Classical Approach Our Approach System Architecture Conclusions

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 3

Preliminaries:XML Functional Dependency

Left Part Right Part

{p1, p2,…pn} q

XML Paths…

course

name year

"DatabasesSystems"

"2005"

faculty

professor

"Robinson"

course

name year

"DatabasesSystems"

"2006"

professor

"Robinson"

course

name year

"Programming""2006"

professor

"Brown"

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/faculty/course/name, /faculty/course/year /faculty/course/name, /faculty/course/year /faculty/course/professor /faculty/course/professor

XML Tree:XML Tree:

XFD:XFD:

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Approximate Functional Dependencies for XML 4

Preliminaries:Tuples

{/faculty/course/name/#text, /faculty/course/professor/#text}

course

name year

"DatabasesSystems"

"2005"

faculty

professor

"Robinson"

course

name year

"DatabasesSystems"

"2006"

professor

"Robinson"

course

name year

"Programming""2006"

professor

"Brown"

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course

name

faculty

professor

1

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"DatabasesSystems"

4"Robinson"8

course

name

faculty

professor

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"DatabasesSystems"

"Robinson"11 15

course

name

faculty

professor

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"Programming" "Brown"18 22

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 5

Inference Problem

XMLDocument

XMLFunctional Dependencies

XMLDocument

XFD

Is it satisfied?

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 6

Classical Approach: XFD Satisfaction

XMLDocumen

t

XFD f: {p1, p2,…pn} q

Tuples {t1, t2, …, tm}

ti, tjAre ti, tj equal w.r.t.

the left part of f?

(ti, tj) satisfies f

yes

no

(ti, tj) does not satisfy f

yes

no

f is not satisfiedby the XML Document

f is satisfiedif and only if

each pair of tuplessatisfies f

Are ti, tj equal w.r.t.the right part of f?

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 7

Classical Approach: XFD Satisfaction

course

name year

"DatabasesSystems"

"2005"

faculty

professor

"Robinson"

course

name year

"DatabasesSystems"

"2006"

professor

"Robinson"

course

name year

"Programming""2006"

professor

"Brown"

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/faculty/course/name/#text /faculty/course/name/#text /faculty/course/professor/#text /faculty/course/professor/#text ??

XML Tree:XML Tree:

course

name

faculty

professor

1

2

3 7

"DatabasesSystems"

4"Robinson"8

course

name

faculty

professor

1

9

10 14

"DatabasesSystems"

"Robinson"11 15

course

name

faculty

professor

1

16

17 21

"Programming" "Brown"18 22

XFD:XFD:

Tuples:Tuples:

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Approximate Functional Dependencies for XML 8

Classical Approach: XFD Satisfaction/faculty/course/name/#text /faculty/course/name/#text /faculty/course/professor/#text /faculty/course/professor/#text

course

name

"DatabasesSystems"

"Robinson"

faculty

professor

1

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course

name

"DatabasesSystems"

"Robinson"

faculty

professor

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course

name

"Programming" "Brown"

faculty

professor

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??Yes

1 2 3

(1,2): (1,3): (2,3):

= =≠ ≠

ok ok ok

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Approximate Functional Dependencies for XML 9

Classical Approach: XFD Satisfaction/faculty/course/name /faculty/course/book ?YES!

1 2

3

=

==

=

(1,2): ok (1,3): ok (2,3): ok

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 10

Classical Approach: Flaw 1/faculty/course/name /faculty/course/book ?NO!

1 2

3

==

(1,3): no

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Our Approach: approximation/faculty/course/name /faculty/course/book ?YES!

≈dist>

1 2

3

≈dist<

≈dist<≈dist>

(1,3): ok (1,2): ok (2,3): oksatisfied

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 12

Classical Approach: Flaw 2/faculty/course/professor /faculty/course/semester ?YES!

1 2

3

= =

= =

(1,2): ok (1,3): ok (2,3): ok

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 13

Our Approach: approximation/faculty/course/professor /faculty/course/semester ?NO!

1 2

3≈

(1,3): NO

≈

Notsatisfied

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 14

Classical Approach: Flaw 3/faculty/course/name /faculty/course/credits ?NO!

1 2 3

4 5

(1,2): no (1,3): no (1,4): ok (1,5): ok

(2,3): ok (2,4): ok (2,5): ok (3,4): ok (3,5): ok (4,5): ok

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 15

Our Approach: approximation/faculty/course/name /faculty/course/credits ?NO!

1 2 3

4 5

(1,2): no (1,3): no (1,4): ok (1,5): ok

(2,3): ok (2,4): ok (2,5): ok (3,4): ok (3,5): ok (4,5): ok

≈ ≈Notsatisfied

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 16

Our Approach: approximation/faculty/course/name /faculty/course/credits ?YES!

1 2 3

4 5

(2,3): ok (2,4): ok (2,5): ok (3,4): ok (3,5): ok (4,5): ok

(1,2): no (1,3): no (1,4): ok (1,5): ok satisfied

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YES!

Our Approach: approximation/faculty/course/name /faculty/course/credits

1 2 3

4 5

satisfiedSet of tuples: {1,2,3,4,5}

Maximal set of tuples-satisfying the XFD: {2,3,4,5}

4/5 >

September 29 - October 3, 2007 Varna (Bulgaria)

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Our Approach: Approximate Inference

XMLDocument XML

Functional Dependencies

XMLDocument

XFD

Is it ()-satisfied?

September 29 - October 3, 2007 Varna (Bulgaria)

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Our Approach:XFD Approximate Satisfaction

XMLDocumen

t

XFD f: {p1, p2,…pn} q

Tuples {t1, t2, …, tm}

ti, tjAre ti, tj similar

w.r.t. the left part of f?

(ti, tj) -satisfies f

yes

noyes

no(ti, tj) does not -satisfy f

THENf is not satisfied by the XML Document

Are ti, tj similarw.r.t. the right part of f?

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 20

Our Approach:XFD Approximate Satisfaction

XMLDocumen

t

XFD f: {p1, p2,…pn} q

Tuples {t1, t2, …, tm}

Is this size at leastthe % of the totalnumber of tuples?

yesno

f is ()-satisfied bythe XML document

Compute the size of the maximalset of tuples -satisfying f

f is not ()-satisfied bythe XML document

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 21

Fox System Architecture

XMLDoc

GraphicalUser Interface

XFD CheckerXFD GeneratorPreprocessing

Module

XFDsapprox

satisfied

September 29 - October 3, 2007 Varna (Bulgaria)

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Conclusions

The concept of approximate satisfaction of XFDs has been motivated and discussed

A system to infer such XFDs has been presented

September 29 - October 3, 2007 Varna (Bulgaria)

Approximate Functional Dependencies for XML 23