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Add advanced database chapter 2

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Yorick Barbanneau 2022-01-18 00:25:30 +01:00
parent 94978b8cf7
commit fe903401de
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---
title: "Base de données avancées : Introduction au modèle relationnel"
date: 2022-01-11
tags: ["définitions", "modèle relationnel", "relation"]
categories: ["Base de données avancées", "Cours"]
mathjax: true
---
Le point de départ de notre introduction est une unique relation universelle
contenant tous les attributs comme dans l'exemple ci-dessous:
| Vol | Avion | Capacité |
| :---: | :---: | :---: |
| IT6543 | Airbus A320 | 310 |
| AF4576 | Airbus A320 | 310 |
| EF3490 | Boeing 777 Max | 210 |
| RA7889 | Airbus A330 | 335 |
| RU7854 | Tupolev Tu-204 | 210 |
Cette modélisation n'est pas sans poser plusieurs problèmes:
* **L'espace de stockage** : sur cette petite relation, certaines données sont
enregistrées plusieurs fois.
* **Mise à jour** : si ont doit changer la capacité des *Airbus A320* suite un
réaménagement par exemple. Il faudra passer en revue l'ensemble des
enregistrements de la table.
* **Insertion incohérente** : et si on insère un avion sans vol.
* **Lors de la suppression** d'un enregistrement avec un seul type d'avion,
comme l'exemple du *Tupolev Tu-204*, on supprime aussi l'avion.
## Le modèle relationnel
Définis par E.F. Codd, le modèle relationnel se veut **indépendant** de la
représentation physique des données avec une assise mathématique forte : le
concept mathématique de relation en théorie des ensembles.
Il se base donc sur **l'algèbre relationnel** et le produit cartésien. Ce modèle
défini une façon de représenter les données, les opérations possibles et les
outils pour assurer la consistance des données.
Les objectifs sont multiples:
* éliminer les comportements anormaux
* éliminer les données redondantes
* avoir une meilleurs compréhension des relations sémantiques entre les données
## Conception d'un schéma relationnel
Lors de la conception, il nous faut éliminer toutes les anomalies de la relation
universelle afin de faciliter la manipulation des relations qui en découlent. On
parles alors de **normaliser les relations**.
Lors de la décomposition il faut veiller à obtenir un schéma qui :
* conserve l'ensemble des données
* conserve un minimum les contraintes d'intégrité tout en respectant le réel
perçu (à l'aide des formes normales?)
* éliminer les anomalies
## Schéma de base de données
Un schéma de base de données est un ensemble de schémas liés par des dépendances
référentielles : des attributs communs et des dépendances d'inclusions.
Une base de données est alors un ensemble de relations associé au schéma de base
de données et vérifiant toutes ses relations.
![Schema de base de données compagnie aérienne](./images/schema_bdd.svg)
Dans le schéma ci-dessus :
* \\( planning.num_vol \subseteq vols.num_vols \\)
* \\( planning.matricule \subseteq pilotes.matricule \\)
* \\( planning.num_avion \subseteq avions.num_serie \\)
## contraintes d'intégrité
Tout schéma de base de données doit être conçu pour imposer le respect d'un
maximum de **contraintes d'intégrité** du réel perçu. Les contraintes
d'intégrités sont des expressions logiques devant être satisfaites à tout
instant par une instance de la base de données. Ces contraintes sont de plusieurs
types:
* sur les attributs : domaines vides
* sur les *n_uplets* : la valeur d'un attribut peut dépendre des valeurs d'autres
attributs dans le cas d'un vol, il ne peux pas atterrir avant d'avoir
décoller (en UTC bien entendu!)
* sur les relations : les clefs, les cardinalités
* sur la base de données : clef étrangères
* temporelles : évolution chronologique ( diplômes, état civil)
On va alors chercher à minimiser le nombre des contraintes tout en restant
équivalents aux contraintes d'origines.
## la notion de clé
Une relation étant un ensemble de *n_uplets*, et comme un ensemble n'a pas
d'éléments en double, on peut alors dire que chaque *n_uplet* est unique. Pour en
identifier un *n_uplet* sans fournir toutes ses valeurs tout en respectant leur
unicité, **une clé est nécessaire**.
Par définition, **une clé** est donc un groupe minimum d'attributs qui
déterminent de façon unique un *n_uplet*. Tout relation possède au moins une clé
: l'ensemble de ses attributs.
Si une relation possède plusieurs **clefs candidates**, on en choisi une qui
sera privilégiée : **la clé primaire**. Bien entendu aucun des attributs d'une
clé primaire ne peux avoir **de valeur nulle**.