1. Jennifer Widom Recursion in SQL Nonlinear and Mutual Recursion

2. Jennifer Widom SQL With Recursive Statement With Recursive R1 As (query-1), R2 As (query-2),... Rn As (query-n) Nonlinear & Mutual Recursion

3. Jennifer Widom SQL With Recursive Statement With Recursive R As ( base query Union recursive query ) Nonlinear & Mutual Recursion

4. Jennifer Widom Linear Recursion With Recursive R As ( base query Union recursive query ) Nonlinear & Mutual Recursion

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

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

7. Jennifer Widom 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 Nonlinear & Mutual Recursion

8. Jennifer Widom SQL With Recursive Statement With Recursive R1 As (query-1), R2 As (query-2),... Rn As (query-n) Nonlinear & Mutual Recursion

9. Jennifer Widom Mutual Recursion With Recursive R1 As (query-1), R2 As (query-2),... Rn As (query-n) Nonlinear & Mutual Recursion

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

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

12. Jennifer Widom Nonlinear & Mutual Recursion Example: Hubs & Authorities

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

14. Jennifer Widom 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) Nonlinear & Mutual Recursion