Approximate Functional Dependencies for XML Data Fabio Fassetti, Bettina Fazzinga DEIS, University...
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Transcript of Approximate Functional Dependencies for XML Data Fabio Fassetti, Bettina Fazzinga DEIS, University...
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:
September 29 - October 3, 2007 Varna (Bulgaria)
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
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
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:
September 29 - October 3, 2007 Varna (Bulgaria)
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
2
3
4
7
8
course
name
"DatabasesSystems"
"Robinson"
faculty
professor
1
9
10
11
14
15
course
name
"Programming" "Brown"
faculty
professor
1
16
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??Yes
1 2 3
(1,2): (1,3): (2,3):
= =≠ ≠
ok ok ok
September 29 - October 3, 2007 Varna (Bulgaria)
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
September 29 - October 3, 2007 Varna (Bulgaria)
Approximate Functional Dependencies for XML 11
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
September 29 - October 3, 2007 Varna (Bulgaria)
Approximate Functional Dependencies for XML 17
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)
Approximate Functional Dependencies for XML 18
Our Approach: Approximate Inference
XMLDocument XML
Functional Dependencies
XMLDocument
XFD
Is it ()-satisfied?
September 29 - October 3, 2007 Varna (Bulgaria)
Approximate Functional Dependencies for XML 19
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)
Approximate Functional Dependencies for XML 22
Conclusions
The concept of approximate satisfaction of XFDs has been motivated and discussed
A system to infer such XFDs has been presented