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Trees and Hierarchies in SQL

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Trees and Hierarchies in SQL
       by Eduard Hildebrandt
In most projects we have to deal with
       some kind of trees or hierarchies!

Think about…
   • Categories
   • Organisation
   • Threads
   • Folders
   • Components
   •…
How can we store an retrieve trees and hierarchies
     effenciently from relational databases?
Agenda

• Adjacency List Model
• Closure Table Model
• Path Enumeration Model
• David Chandler Model
• Modified David Chandler Model
• Nested Set Model
• Hyprid Model
• Frequent Insertion in Nested Sets
What is a „tree“?
A tree is a connected, undirected, acyclic grap.



                                               A

                                   B                   C

                        D          E               F       G   H

                                                   I
What is a „tree“?
A tree is a connected, undirected, acyclic grap.



                                               A

                                   B                   C

                        D          E               F       G   H

                                                   I           X

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Trees and Hierarchies in SQL

  • 1. Trees and Hierarchies in SQL by Eduard Hildebrandt
  • 2. In most projects we have to deal with some kind of trees or hierarchies! Think about… • Categories • Organisation • Threads • Folders • Components •…
  • 3. How can we store an retrieve trees and hierarchies effenciently from relational databases?
  • 4. Agenda • Adjacency List Model • Closure Table Model • Path Enumeration Model • David Chandler Model • Modified David Chandler Model • Nested Set Model • Hyprid Model • Frequent Insertion in Nested Sets
  • 5. What is a „tree“? A tree is a connected, undirected, acyclic grap. A B C D E F G H I
  • 6. What is a „tree“? A tree is a connected, undirected, acyclic grap. A B C D E F G H I X
  • 7. What is a „tree“? A tree is a connected, undirected, acyclic grap. A B C D E F G H I
  • 8. What is a „tree“? A tree is a connected, undirected, acyclic grap. A B C D E F G H I
  • 9. Adjacency List Model A B C D E F G H I title parent Creating the table: CREATE TABLE nodes A null (title VARCHAR(255) NOT NULL PRIMARY KEY, B A parent VARCHAR(255)); C A Finding the root node: D B SELECT * FROM nodes E B WHERE parent IS NULL; F C Finding the leaf nodes: G C SELECT node1.* H C FROM nodes AS node1 LEFT JOIN node AS node2 ON node1.title = node2.parent I F WHERE node2.title = ‘A’;
  • 10. Adjacency List Model UPDATE anomalies A B C D E F G H title parent I A null UPDATE nodes SET title = ‘X’ B A WHERE title = ‘C’; C A D B START TRANSACTION; UPDATE nodes E B SET title = ‘X’ WHERE title = ‘C’; F C UPDATE nodes G C SET parent = ‘X’ WHERE parent = ‘C’; H C COMMIT; I F
  • 11. Adjacency List Model INSERT anomalies INSERT INTO nodes (title, parent) VALUES (‘X’, ‘Y’), X Y (‘Y’, ‘X’); INSERT INTO nodes (title, parent) VALUES X (‘X’, ‘X’); Parent must exist: ALTER TABLE nodes ADD CONSTRAINT parent_fk FOREIGN KEY (parent) REFERENCES nodes (id); Node can not be it‘s own parent: CHECK (title <> parent) Prevent double connections: UNIQUE (title, parent) Connected graph (edges = nodes – 1): CHECK ((SELECT COUNT(*) FROM nodes) – 1 = SELECT COUNT(parent) FROM nodes; One root only: CHECK ((SELECT COUNT(*) FROM nodes WHERE parent IS NULL) = 1);
  • 12. Adjacency List Model DELETE anomalies DELETE FROM nodes WHERE title = ‘C’; A B C D E F G H I
  • 13. Adjacency List Model DELETE anomalies What happens with nodes F, G, H and I? A B ? D E F G H I ALTER TABLE nodes ADD CONSTRAINT parent_fk FOREIGN KEY (parent) REFERENCES nodes (id) ON DELETE ...;
  • 14. Adjacency List Model DELETE anomalies Solution 1: delete all children A B C D E F G H I
  • 15. Adjacency List Model DELETE anomalies Solution 2: move children to the level of the parent A B F G H D E I
  • 16. Adjacency List Model DELETE anomalies Solution 3: replace parent with the first child A B F D E I G H
  • 17. Adjacency List Model with self -references A B C D E F G H title parent I A A Creating the table: CREATE TABLE nodes B A (title VARCHAR(255) NOT NULL PRIMARY KEY, parent VARCHAR(255) NOT NULL); C A D B E B Avoids NULL in the parent column! F C G C H C I F
  • 18. Path Enumeration Model A B C D E F G H I title path Creating the table: CREATE TABLE nodes A A (title VARCHAR(255) NOT NULL PRIMARY KEY B A/B -- don’t use a separater in primary key CHECK (REPLACE (title, ‘/’, ‘’) = title, C A/C path VARCHAR(1024) NOT NULL); D A/B/D E A/B/E F A/C/F G A/C/G H A/C/H I A/C/F/I
  • 19. Closure Table Model A B C D E F G H ID parent Ancestor Descendant 1 A 1 2 2 B 1 4 3 C 1 5 4 D 2 4 5 E 2 5 6 F 1 3 7 G 1 6 8 H 1 7 1 8
  • 20. David Chandler Model A B C D E F G H ID T L1 L2 L3 Creating the table: CREATE TABLE nodes 1 A 1 0 0 (id INTEGER NOT NULL PRIMARY KEY 2 B 1 1 0 title VARCHAR(255) NOT NULL L1 INTEGER NOT NULL, 3 C 1 2 0 L2 INTEGER NOT NULL, L3 INTEGER NOT NULL); 4 D 1 1 1 5 E 1 1 2 Algorithm is patened by David Chandler! 6 F 1 2 1 7 G 1 2 2 Hierarchy level is fixed! 8 H 1 2 3
  • 21. Modified David Chandler Model A B C D E F G H ID T L1 L2 L3 Creating the table: CREATE TABLE nodes 1 A 1 0 0 (id INTEGER NOT NULL PRIMARY KEY 2 B 1 2 0 title VARCHAR(255) NOT NULL L1 INTEGER NOT NULL, 3 C 1 3 0 L2 INTEGER NOT NULL, L3 INTEGER NOT NULL); 4 D 1 2 4 5 E 1 2 5 Not sure about implecations of David 6 F 1 3 6 Chandlers patent… 7 G 1 3 7 Hierarchy level is fixed! 8 H 1 3 8
  • 22. Nested Set Model 1 A 18 2 B 7 8 C 17 3 D 4 5 E 6 9 F 12 13 G 14 15 H 16 10 I 11 title lft rgt Creating the table: CREATE TABLE nodes A 1 18 (title VARCHAR(255) NOT NULL PRIMARY KEY, B 2 7 lft INTEGER NOT NULL, rgt INTEGER NOT NULL); C 8 17 Finding the root node: D 3 4 SELECT * FROM nodes E 5 6 WHERE lft = 1; F 9 12 Finding the leaf nodes: G 13 14 SELECT * H 15 16 FROM nodes WHERE lft = (MAX(rgt) – 1) I 10 11
  • 23. Nested Set Model 1 A 18 2 B 7 8 C 17 3 D 4 5 E 6 9 F 12 13 G 14 15 H 16 10 I 11 title lft rgt Finding subtrees: A 1 18 SELECT * FROM nodes WHERE lft BETWEEN lft AND rgt B 2 7 ORDER BY lft ASC; C 8 17 Finding path to a node: D 3 4 SELECT * FROM nodes WHERE lft < ? AND rgt > ? E 5 6 ORDER BY lft ASC; F 9 12 G 13 14 H 15 16 I 10 11
  • 24. Hybrid Models Combining models Adjacency List David Chandler Path Enumeration Nested Set Closure Table
  • 25. Nested Set Model Problem: Tree must be reorganized on every insertion (table lock). 1 A 100 2 B 49 50 C 99 D E F G H 3 24 25 48 51 72 73 14 15 16 Possible solution: Avoid overhead with larger spreads and bigger gaps
  • 26. Nested Set Model What datatype shout I use for left and right values? INTEGER FLOAT / REAL / DOUBLE NUMERIC / DECIMAL
  • 27. Nested Set Model with rational numbers 0/5 A 5/5 1/5 B 2/5 3/5 C 4/5 a b a+(b-a)/3 a+2(b-a)/3
  • 28. Nested Set Model with rational numbers 0/5 A 5/5 1/5 B 2/5 3/5 C 4/5 16/25 D 17/25 T ln ld rn rd A 0 5 5 5 Adding an aditional child node is alway possible. B 1 5 2 5 No need to reorganize the table! C 3 5 4 5 D 16 25 17 25
  • 29. Nested Set Model Binary Fraction node X Y 1 1 1/2 1.1 1 3/4 1.1.1 1 7/8 1.1.1.1 1 15/16 1.1.2 7/8 13/16 1.1.3 13/16 25/32 1.2 3/4 5/8 1.2.1 3/4 11/16 1.3 5/8 9/16
  • 30. Literature Titel: Trees and Hierarchies in SQL Autor: Joe Celko Verlag: Morgan Kaufmann ISBN: 1558609202
  • 31. Q&A