Difference between revisions of "Functional Dependencies"
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A≡single is also a [https://en.wikipedia.org/wiki/Super_key super key] and [https://en.wikipedia.org/wiki/Primary_key primary key] | A≡single is also a [https://en.wikipedia.org/wiki/Super_key super key] and [https://en.wikipedia.org/wiki/Primary_key primary key] | ||
| − | With a slightly modified query we'll see that wikidata uses a [https://en.wikipedia.org/wiki/Surrogate_key surrogate key] as the primary key for | + | With a slightly modified query we'll see that wikidata uses a [https://en.wikipedia.org/wiki/Surrogate_key surrogate key] as the primary key for all items. |
| − | + | Querying Wikidata's graph data more often than not leads to results that need to be normalized to be useful in the context of relational databases. | |
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=== result === | === result === | ||
Revision as of 10:01, 15 June 2022
Notation
In Database theory: [math]\{A,B\}\to \{C,D\}[/math] is abbreviated to: [math]AB\to CD[/math]
Simple hierarchical Example
9 single entries for 2022 sorted by social media followers
SPARQL query
result as of 2022-06-13
| 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]
functional dependencies diagram
The following diagram shows the functional dependencies of this example. The nodes represent the attributes and the edges the dependencies.
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 |
Candidate Keys
There is only a single candidate key: A≡single
It is the only attribute that has the full set of attributes as it's closure. A≡single is also a super key and primary key
With a slightly modified query we'll see that wikidata uses a surrogate key as the primary key for all items. Querying Wikidata's graph data more often than not leads to results that need to be normalized to be useful in the context of relational databases.
result
Synthesis
Links
Wikipedia
The following graph shows some relevant wikipedia articles. If the nodes are not clickable in your browser you might want to open the svg image in a separate tab to get a clickable version of this graph.
- https://en.wikipedia.org/wiki/Category:Database_theory
- https://en.wikipedia.org/wiki/Functional_dependency
- https://en.wikipedia.org/wiki/Database_normalization
- https://en.wikipedia.org/wiki/First_normal_form
- https://en.wikipedia.org/wiki/Second_normal_form
- https://en.wikipedia.org/wiki/Third_normal_form
- https://en.wikipedia.org/wiki/Boyce%E2%80%93Codd_normal_form
- https://en.wikipedia.org/wiki/Lossless_join_decomposition
- https://en.wikipedia.org/wiki/Candidate_key
- https://en.wikipedia.org/wiki/Surrogate_key
- https://en.wikipedia.org/wiki/Superkey