From 6eb80d0b40de95922a381f4924b8ad5d05bd5e27 Mon Sep 17 00:00:00 2001 From: =?utf8?q?Kim=20Nguy=E1=BB=85n?= Date: Mon, 31 Mar 2014 11:51:37 +0200 Subject: [PATCH] Ajout du cours 5 --- bd/bd04.xhtml | 7 +- bd/bd05.xhtml | 410 ++++++++++++++++++++++++++++++++++++++++ bd/left_deep.svg | 427 ++++++++++++++++++++++++++++++++++++++++++ bd/pdf/bd05.pdf | Bin 0 -> 437240 bytes bd/pdf/bd05_print.pdf | Bin 0 -> 422980 bytes bd/simple_plan.svg | 254 +++++++++++++++++++++++++ bd/simple_plan1.svg | 313 +++++++++++++++++++++++++++++++ bd/simple_plan2.svg | 331 ++++++++++++++++++++++++++++++++ 8 files changed, 1740 insertions(+), 2 deletions(-) create mode 100644 bd/bd05.xhtml create mode 100644 bd/left_deep.svg create mode 100644 bd/pdf/bd05.pdf create mode 100644 bd/pdf/bd05_print.pdf create mode 100644 bd/simple_plan.svg create mode 100644 bd/simple_plan1.svg create mode 100644 bd/simple_plan2.svg diff --git a/bd/bd04.xhtml b/bd/bd04.xhtml index 127462c..15fc600 100644 --- a/bd/bd04.xhtml +++ b/bd/bd04.xhtml @@ -55,6 +55,7 @@

Motivation

Principe d'évaluation d'une requête

+
  1. Parsing de la requête
  2. Traduction en arbre @@ -76,7 +77,9 @@
  3. (Éventuellement mise à jour des statistiques)

Avant de s'intéresser à l'évaluation complète d'une requête, - on étudie l'évaluation des opérateurs et leur coût respectifs

+ on étudie l'évaluation des opérateurs et leur coût + respectifs

+

Algorithmes de jointure

@@ -85,7 +88,7 @@ FROM people,role WHERE people.pid = role.pid; -

Opéreeation fondamentale utilisée +

Opération fondamentale utilisée par toutes les applications BD.
L'AR nous dit que R &join; S = σ=(R x T), mais c'est très inefficace, on veut optimiser ce cas! diff --git a/bd/bd05.xhtml b/bd/bd05.xhtml new file mode 100644 index 0000000..9d7e4bf --- /dev/null +++ b/bd/bd05.xhtml @@ -0,0 +1,410 @@ + +∈"> + ∉"> + + +] + > + + + Optimisation de requêtes + + + + + + + + + + + + + + + + + + + + +

+ +

Motivation et introduction

+
+

Principe d'évaluation d'une requête

+
+
    +
  1. Parsing de la requête
  2. +
  3. Traduction en arbre + d'opérateurs de l'algèbre + relationnelle (π, + σ, ⨝, … )
  4. +
  5. Optimisation : +
      +
    1. Génération de plans + d'évaluation (en + réordonnant les opérations élémentaires)
    2. +
    3. Estimation du coût de chacun des + plans (en fonction du coût + des opérations élémentaires)
    4. +
    5. Choix du plan le plus efficace
    6. +
    +
  6. +
  7. Évaluation du plan choisi
  8. +
  9. (Éventuellement mise à jour des statistiques)
  10. +
+

On va voir comment optimiser l'évaluation d'une requête

+
+
+
+

Exemple pour la suite du cours

+ Sailors(mid: integer, sname: string, rating: integer, age: real); + Reserves(sid: integer, bid: integer, day: date, rname: string); + Boats(bid: integer, bname: string, capacity: integer); + +
    +
  • Sailors: 50 octets/enr., 80 enr/page, 500 + pages
  • +
  • Reserves: 40 octets/enr., 100 enr/page, 1000 + pages
  • +
  • Boats: non utilisé dans la suite
  • +
+
+
+

Généralités

+

Un plan d'exécution de requête est un arbre + dont les noeuds sont des opérateurs de l'algèbre relationnelle + annotés avec un algorithme particulier. +

+
    +
  • Pour une requête donnée, quels plans doit-on considérer + ?
  • +
  • Comment peut on estimer le coût total d'un plan
  • +
+

Idéalement, on veut trouver le meilleur plan. En pratique, on + choisira le moins pire!

+
+
+

Exemple

+ + SELECT S.sname + FROM Reserves R, Sailors S + WHERE R.sid = S.sid AND bid = 100 AND rating > 5 + +

+
    +
  • Cout: 500+500*1000 E/S (pourquoi ?)
  • +
  • Plusieurs occasions manquées : pas d'utilisation d'index, on + aurait pu pousser la selection sous la jointure, …
  • +
  • Notre but est de trouver des plans d'exécution plus efficaces + qui calculent le même résultat
  • +
+
+
+

Plan alternatif 1 (sans index)

+

+

On pousse la sélection sous la jointure (car + selection AND). On suppose qu'on a 100 + bateaux, 10 notes et distributions uniformes.

+
    +
  • Scan Reserves (1000 E/S) et écriture de 10 pages dans T1
  • +
  • Scan Sailors (500 E/S) et écriture de 250 pages dans T2
  • +
  • Tri T1 (3*10 E/S), Tri T2 (8*250 E/S), fusion (10+250 E/S)
  • +
  • Total: 4050 E/S
  • +
  • Si on pousse la projection, T1 ne contient que sid, T2 + uniquement sid et sname (cout < 2000 E/S)
  • +
+
+
+

Plan alternatif 2 (avec index)

+

+

On suppose un hash-index groupant sur bid +

+
    +
  • Accès au premier enregistrement bid=100 1.2 E/S
  • +
  • Accès aux suivants: 9 E/S
  • +
  • sid est une clé pour Sailors. On a un hash-index dessus + (forcément non-groupant)
  • +
  • Pour chacun des 10 * 100 enr. tels que bid=100 on + cherche l'enregistrement de Sailors avec le même sid (1.2 + E/S/enr)
  • +
  • Coût total: 1000 * 1.2 + 10.2 = 1210 E/S
  • +
+
+
+

Algorithme général de choix de plan

+
  • Cas mono-relation (une seule table dans le FROM): +
    1. On énumère tous les plans (en tenant compte des + équivalences de l'algèbre relationnelle)
    2. +
    3. On calcule le coût de chaque plan
    4. +
    5. On choisit le plan de moindre coût
    6. +
    +
  • +
  • Cas multi-relations (plusieurs tables dans le FROM): +
    1. Trop de plan pour les énumérer tous, on choisit des arbres + ayant une certaine forme
    2. +
    3. On calcule le coût de chaque plan
    4. +
    5. On choisit le plan de moindre coût
    6. +
    +
  • +
  • On sait (cours 4) estimer le coût d'un opérateur en fonction de + la taille de l'entrée. On va enchaîner les opérateurs donc il faut + estimer la taille du résultat pour calculer + le coût de l'opérateur suivant!
  • +
+
+

Estimation de coût

+
+

Statistiques et catalogues

+

On a besoin d'informations numériques sur les relations et les + indexes. Un catalogue contient en général:

+
  • Le nombre d'enregistrements (NEnr) et le + nombre de pages (NPages) de la relation. +
  • +
  • Le nombre de clés distinctes (NClés) pour les + indexes ainsi que leur taille en pages
  • +
  • La hauteur ainsi que les clés min/max dans l'index, pour les + arbres
  • +
+

Les catalogues sont mis à jours périodiquement mais pas à chaque + mise à jours, pour ne pas impacter les performances.

+
+
+

Estimation du nombre de résultats et facteur de réduction

+

On considère une requête de la forme:

+ SELECT attributs FROM tables WHERE e1 AND … AND en + +
  • La taille maximale TMax du résultat est le produit des tailles des + tables se trouvant dans le FROM
  • +
  • Le facteur de réduction de chaque expression e + caractérise l'impact de ce terme sur la taille du résultat
  • +
  • La taille finale du résultat est approximée par: TMax * + RF1 * … * RFn
  • +
+

On fait la supposition que les expressions sont indépendantes.
+Exemples de facteurs de réduction: +

+
  • att = valeur : 1 / + NClés si att este une clé pour un index I
  • +
  • att1 = att2 : 1/Max(NClé(I1), + NClé(I2)) (avec atti une clé + de Ii)
  • +
  • att > valeur : (Max(I)-valeur)/(Max(I) - Min(I)) +
  • +
+
+
+

Équivalences de l'algèbre relationnelle

+

Permet de réordonner les jointures et de « pousser » les sélections + et les projections sous les jointures

+
    +
  • Sélections : +
      +
    • σc1∧…∧cn(R) + ≡ + σc1(… (σcn(R))) [Cascade] +
    • +
    • + σc1c2(R)) + ≡ + σc2c1(R)) + [Commutativité] +
    • + +
    +
  • +
  • Projections : +
      +
    • πa1, …, an( + …(πz1, …, zm(R)) + ≡ + πa1, …, an(R) [Cascade] +
    • + +
    +
  • +
  • Jointures : +
      +
    • R &join; (S &join; T) ≡ (R &join; S) &join; T [Associativité] +
    • +
    • (R &join; S) ≡ (S &join; R) [Commutativité] +
    • +
    +
  • +
+
+
+

Autres équivalences

+
    +
  • +Une projection commute avec une selection qui utilise uniquement + les attributs de la projection
  • +
  • Une selection entre des attributs de deux arguments d'un + produit cartésien peut être converti en jointure: + σφ (R × S) ≡ R &join;φ S +
  • +
  • Une selection sur des attributs de R commute avec la + jointure R&join;S (c'est à dire: σ(R&join;S) ≡ σ(R)&join;S ) +
  • +
  • Règle similaire pour pousser les projections sous jointure
  • +
+
+

Énumération de plans

+
+

Modèle de calcul

+

+ Les SGBD modernes utilisent un modèle de + calcul pull. L'opérateur le plus « haut » (racine) + dans l'arbre de requête « tire » (pull) le résultat de ses + sous-arbres (similaire à l'appel de next sur les iterateurs + de la bibliothèque standard Java). Cela permet + de pipeliner les opérateurs. Certains opérateurs « + bloquent » le pipeline (en particulier les tris et + aggrégats). +

+ +
+
+

Cas mono-relation

+

Dans le cas mono-relation (i.e. sans jointure), la requête est + composée forcément de selections, projections et aggrégats + (max, count, average, …)

+
    +
  1. Pour chaque sous-terme, on considère tous les accès possibles + (scan, utilisation de l'index, …) et on prend le moins coûteux
  2. + +
  3. Les opérateurs restants sont calculé à la volée (en + pipelinant les opérations) +
  4. +
+
+
+

Estimation du coût pour les plans mono-relation

+
    +
  • Si on a un index I pour une selection sur clé primaire : + Hauteur(I) + 1 pour un arbre B+, 1.2 + pour un hash-index
  • +
  • Si on a un index I groupant pour plusieurs + selection σ1, …, σn :
    + (NPages(I) + NPages(R))* RF(σ1) * … * RF(σn) +
  • +
  • Si on a un index I non-groupant pour plusieurs + selection σ1, …, σn :
    + (NPages(I) + NEnr(R))* RF(σ1) * … * RF(σn) +
  • +
  • Scan séquentiel à R: NPages(R)
  • +
+
+
+

Exemple de calcul de coût

+ SELECT S.sid FROM Sailors S WHERE S.rating = 8; + πsidrating = 8(R)) +
    +
  • Avec un index sur rating: +
      +
    • Groupant: 1/NClés(I) * (NPages(I) + + NPages(R)). Avec des valeurs numériques: 1/10 * + (50+500) = 55 E/S
    • +
    • Non-groupant: 1/NClés(I) * (NPages(I) + + NEnr(R)). Avec des valeurs numériques: 1/10 * + (50+40000) = 4005 E/S
    • +
    +
  • +
  • Scan : on récupère toutes les pages et on filtre: 500 E/S
  • +
+

Note: Une fois que l'on a sélectionné un enregistrement, + la projection est « gratuite » (en terme d'E/S) car le résultat n'a + pas à être sauvé dans une table temporaire

+
+
+

Requêtes multi-relations

+
  • Les choix vont être guidé par les jointures
  • +
  • Si on considère uniquement n jointures (pas de projections ni + de selections dans le plan de requête). Le nombre de plans possible + est le nombre d'arbre binaires ayant n noeuds internes + (exponentiel en n, exactement: nombre de Catalan + d'indice n). Beaucoup trop pour les énumérer tous. +
  • +
  • On se restreint aux arbres gauches en profondeur qui + permettent d'énumérer tous les plans complètement + « pipelinable » +
  • +
+

+

Ce ne sont que des heuristiques pour réduire l'espace de + recherche, on n'est pas sur d'avoir la solution optimale!

+
+
+

Énumération des plans gauches en profondeur 1/2

+

Toujours exponentiel (mais moins)

+

Tous les arbres différent maintenant dans l'ordre dans lequel on + fait les jointures, la méthode d'accès pour chaque relation et les + algorithmes de jointure utilisés

+

On applique l'heuristique suivante:

+
    +
  1. 1ère passe: on trouve la meilleure manière de calculer + chaque relation individuellement +
  2. +
  3. 2ème passe: on trouve la meilleure manière de joindre + deux à deux les résultats de la passe 1 +
  4. +
  5. nème passe: on trouve la meilleure manière de joindre + deux à deux les résultats de la passe (n-1) +
  6. +
+

Comment sélectionner les « meilleurs » jointures + ? On garde pour chaque ordre de + résultat intermédiaire celle de moindre coût +

+
+
+

Énumération des plans gauches en profondeur 2/2

+

Exemple: si on a la possibilité de faire une jointure itérative de + cout 1000, une jointure par hash de coût 500 et une jointure + sort-merge de coût 1500, on garde les version hash + et sort-merge (car il est possible que le fait d'avoir les + résultats déjà trié rendent le coût moindre à l'étape suivante) +

+

On garde les ORDER BY, GROUP BY, aggrégats, … + pour la fin, en profitant si possible des ordres des résultats faits + par les jointures précédentes

+

On évite tant que possible de faire des produits cartésiens (en + poussant les selections par exemple)

+
+
+

Requêtes imbriquées

+ + SELECT … FROM … WHERE + … e AND EXISTS (SELECT … WHERE … FROM …) + +

On optimise d'abord la requête la plus « interne »

+

On optimise ensuite la requête englobante en utilisant prenant en + compte le coût de la requête interne pour chaque « évaluation » du + WHERE +

+
+ + diff --git a/bd/left_deep.svg b/bd/left_deep.svg new file mode 100644 index 0000000..d62df1a --- /dev/null +++ b/bd/left_deep.svg @@ -0,0 +1,427 @@ + + + + + + + + + + + + image/svg+xml + + + + + + + + ⨝ + A + B + + + ⨝ + C + + + ⨝ + D + + + ⨝ + A + B + + + ⨝ + C + + + ⨝ + D + + + ⨝ + A + B + + + ⨝ + C + + + ⨝ + D + + + + OK + Potentiellement bloquant + Identique au premier + + diff --git a/bd/pdf/bd05.pdf b/bd/pdf/bd05.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3b241152ca784b4c3381a08061ffc21834e28bb1 GIT binary patch literal 437240 zcmeFa1yo$iny`&aun-&qG?3u#!CeBu-QC?SxD#B126y)m+}(p)u;3Qle&C$klR0zl z`tQu#JKwsqy3>o!E~a~=B5EUIY)3evrdnMP;7yz^YOC6JE92@`| zaeWIzJ0k$&Ly^og002NEWNc=qZ}aeKrfsJ$ps#DGr~izL>zS>cjlQ<|GpFSDvhPCX zc;Fj{OGoez^|CJgm-*Au)v0-7czRPRrHPaqOT^C5)hz2f z^PGu&8k{{t>JHK!tuYL<@5szZ67K8n;_Cr0ql@_8zluy`yi0XYXq`!>TL%N5S(ZHp z%@MTYX@ZUR9~a7I+GBakGSG$<(wU)h&f!!cEmztLHKX;`hECHvNlT`V1Y&sZg%s?$ 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zXSf({LgIG54_Es&?E}RU#ZtJ&Ugnm;HQx*if3QB_?N + + + + + + + + + + + image/svg+xml + + + + + + + + Reserves + Sailors + + + ⨝ + R.sid=S.sid + + + + σ + bid=100 ∧ rating>5 + + + π + sname + + + + + + + jointure iterativepage à page + à la volée + à la volée + + + diff --git a/bd/simple_plan1.svg b/bd/simple_plan1.svg new file mode 100644 index 0000000..7f2de95 --- /dev/null +++ b/bd/simple_plan1.svg @@ -0,0 +1,313 @@ + + + + + + + + + + + + image/svg+xml + + + + + + + + Reserves + Sailors + + + ⨝ + R.sid=S.sid + + + + π + sname + + + + + + + sort-merge join + à la volée + + + σ + bid=100 + + + + σ + rating>5 + + + Scan, resultatdans temp. T2 + Scan, resultatdans temp. T1 + + diff --git a/bd/simple_plan2.svg b/bd/simple_plan2.svg new file mode 100644 index 0000000..1b85940 --- /dev/null +++ b/bd/simple_plan2.svg @@ -0,0 +1,331 @@ + + + + + + + + + + + + image/svg+xml + + + + + + + Reserves + Sailors + + ⨝ + R.sid=S.sid + + + + π + sname + + + + + + + jointure iterativepar index + à la volée + + + σ + bid=100 + + + + σ + rating>5 + + + + Hash Indexpas de temp. + à la volée + + -- 2.17.1