Difference between revisions of "Functional Dependencies"

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= Attribute Closures =
 
= Attribute Closures =
 +
The attribute closure is the set of all attributes that are "reachable/determinable" from a given attribute node. In this example the results are quite obvious since the
 +
functional dependencies form a tree and the reachable nodes are all nodes of the subtree of a given attribute.
 +
 +
{| class="wikitable" style="text-align: left;"
 +
|+ <!-- caption -->
 +
|-
 +
! attribute  !! closure
 +
|-
 +
| A          || ABCDEFGHIJ
 +
|-
 +
| B          || B
 +
|-
 +
| C          || CDE
 +
|-
 +
| D          || D
 +
|-
 +
| E          || E
 +
|-
 +
| F          || FGH
 +
|-
 +
| G          || G
 +
|-
 +
| H          || H
 +
|-
 +
| I          || I
 +
|-
 +
| J          || J
 +
|}
 +
 
= Synthesis =
 
= Synthesis =
 
* https://www.comp.nus.edu.sg/~lingtw/papers/bernstein.pdf
 
* https://www.comp.nus.edu.sg/~lingtw/papers/bernstein.pdf

Revision as of 09:04, 14 June 2022

Notation

In Database theory: [math]\{A,B\}\to \{C,D\}[/math] is abbreviated to: [math]AB\to CD[/math]

Example

9 single entries for 2022 sorted by social media followers

query

# WF 2022-06-08
# Singles published in 2022
SELECT
?single ?language ?collectionId ?collection ?collectionType ?performerId ?performer ?followerCount ?youtubeVideoId  (year(?publicationDate) as ?publicationYear)
WHERE
{
  # instanceof
  ?singleId wdt:P31 wd:Q134556. # Must be of a single
  ?singleId rdfs:label ?single.
  FILTER(LANG(?single)='en')

  #https://www.wikidata.org/wiki/Property:P361 - part of / ist Teil von
  ?singleId wdt:P361 ?collectionId.
  ?collectionId rdfs:label ?collection.
  FILTER(LANG(?collection)='en')

  # https://www.wikidata.org/wiki/Property:P407 language/ Sprache des Werkes
  ?singleId wdt:P407 ?languageId.
  ?languageId rdfs:label ?language.
  FILTER(LANG(?language)='en')

  # https://www.wikidata.org/wiki/Property:P1651 YouTube-Video-Kennung
  ?singleId wdt:P1651 ?youtubeVideoId.

  ?collectionId wdt:P31 ?collectionTypeId.
  ?collectionTypeId rdfs:label ?collectionType.
  FILTER(LANG(?collectionType)='en').

  # https://www.wikidata.org/wiki/Property:P175 Performer /Interpret
  ?singleId wdt:P175 ?performerId.
  ?performerId rdfs:label ?performer
  FILTER(LANG(?performer)='en')

  # https://www.wikidata.org/wiki/Property:P8687 followers / Follower
  #{
     #SELECT (max(?followerCount) as ?follower)
     #WHERE {
     ?performerId wdt:P8687 ?followerCount.
     #}
     #GROUP BY ?performerId
  #}
  #https://www.wikidata.org/wiki/Property:P577 Publication date / Veröffentlichungsdatum
  ?singleId wdt:P577 ?publicationDate.
  FILTER(year(?publicationDate) = 2022).
} ORDER BY  DESC(?followerCount)
LIMIT 9

try it!

result

A B C D E F G H I J
single language collectionId collection collectionType performerId performer followerCount youtubeVideoId publicationYear
Let Somebody Go English http://www.wikidata.org/entity/Q107597380 Music of the Spheres album http://www.wikidata.org/entity/Q83287 Selena Gomez 65629044 EptPhiK_q0E 2022
As It Was English http://www.wikidata.org/entity/Q111343757 Harry's House album http://www.wikidata.org/entity/Q3626966 Harry Styles 36156370 H5v3kku4y6Q 2022
Let Somebody Go English http://www.wikidata.org/entity/Q107597380 Music of the Spheres album http://www.wikidata.org/entity/Q45188 Coldplay 23541189 EptPhiK_q0E 2022
Bam Bam English http://www.wikidata.org/entity/Q56071495 Camila Cabello singles discography singles discography http://www.wikidata.org/entity/Q47447 Ed Sheeran 17661915 -8VfKZCOo_I 2022
Bam Bam English http://www.wikidata.org/entity/Q111083420 Familia album http://www.wikidata.org/entity/Q47447 Ed Sheeran 17661915 -8VfKZCOo_I 2022
Sacrifice English http://www.wikidata.org/entity/Q110400486 Dawn FM album http://www.wikidata.org/entity/Q2121062 The Weeknd 15549868 VafTMsrnSTU 2022
Out of Time English http://www.wikidata.org/entity/Q110400486 Dawn FM album http://www.wikidata.org/entity/Q2121062 The Weeknd 15549868 2fDzCWNS3ig 2022
Bam Bam English http://www.wikidata.org/entity/Q56071495 Camila Cabello singles discography singles discography http://www.wikidata.org/entity/Q18810940 Camila Cabello 12717885 -8VfKZCOo_I 2022
Bam Bam English http://www.wikidata.org/entity/Q111083420 Familia album http://www.wikidata.org/entity/Q18810940 Camila Cabello 12717885 -8VfKZCOo_I 2022

Functional Dependencies

The functional dependencies in this example are derived from the structure of the SPARQL query

  • A≡single
  • B≡language
  • C≡collectionId
  • D≡collection
  • E≡collectionType
  • F≡performerId
  • G≡performer
  • H≡followerCount
  • I≡youtubeVideoId
  • J≡publicationYear
  • [math]A\to BCFIJ[/math]
  • [math]C\to DE[/math]
  • [math]F\to GH[/math]

[math]R={{\{A,B,C,D,E,F,G,H,I,J\}},{A\to BCFIJ,C\to DE,F\to GH}}[/math] 0x9019d413.png

Attribute Closures

The attribute closure is the set of all attributes that are "reachable/determinable" from a given attribute node. In this example the results are quite obvious since the functional dependencies form a tree and the reachable nodes are all nodes of the subtree of a given attribute.

attribute closure
A ABCDEFGHIJ
B B
C CDE
D D
E E
F FGH
G G
H H
I I
J J

Synthesis

Links

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