1. Recursion in SQL
Nonlinear and Mutual Recursion

2. Nonlinear & Mutual Recursion
SQL With Recursive Statement
With Recursive
R1 As (query-1),
R2 As (query-2),
...
Rn As (query-n)
<query involving R1,…,Rn (and other tables)>

3. Nonlinear & Mutual Recursion
SQL With Recursive Statement
With Recursive
R As ( base query
Union
recursive query )
<query involving R (and other tables)>

4. Nonlinear & Mutual Recursion
Linear Recursion
With Recursive
R As ( base query
Union
recursive query )
<query involving R (and other tables)>

5. Nonlinear & Mutual Recursion
Example: Ancestors
ParentOf(parent,child) Find all of Mary’s ancestors

6. Nonlinear & Mutual Recursion
Example: Ancestors
ParentOf(parent,child) Find all of Mary’s ancestors

7. Nonlinear & Mutual Recursion
Example: Ancestors
ParentOf(parent,child) Find all of Mary’s ancestors
Nonlinear (versus linear)
+ Query looks cleaner
+ Converges faster
– Harder to implement
SQL standard only requires linear

8. Nonlinear & Mutual Recursion
SQL With Recursive Statement
With Recursive
R1 As (query-1),
R2 As (query-2),
...
Rn As (query-n)
<query involving R1,…,Rn (and other tables)>

9. Nonlinear & Mutual Recursion
With Recursive
R1 As (query-1),
R2 As (query-2),
...
Rn As (query-n)
<query involving R1,…,Rn (and other tables)>

10. Nonlinear & Mutual Recursion
Example: Hubs & Authorities
Link(src,dest)
HubStart(node) AuthStart(node)

11. Nonlinear & Mutual Recursion
Example: Hubs & Authorities
Link(src,dest)
HubStart(node) AuthStart(node)

12. Nonlinear & Mutual Recursion
Example: Hubs & Authorities

13. Nonlinear & Mutual Recursion
Example: Recursion with Aggregation
P(x)

14. Nonlinear & Mutual Recursion
SQL With Recursive Statement
Extends expressiveness of SQL
Basic functionality: linear recursion
Extended functionality: nonlinear recursion, mutual recursion
Disallowed: recursive subqueries (negative), aggregation
With Recursive
R1 As (query-1),
R2 As (query-2),
...
Rn As (query-n)
<query involving R1,…,Rn (and other tables)>