The document discusses several models for representing hierarchical or tree-like data structures in relational databases, including adjacency list, closure table, path enumeration, nested set, and various extensions of the David Chandler model. It provides examples of creating tables and querying data for each model, and notes some advantages and limitations of each approach.

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