1. Chapter 14: Query Optimization Database System Concepts 5 th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use

6. Generating Equivalent Expressions Database System Concepts 5 th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use

9. Equivalence Rules (Cont.) 5. Theta-join operations (and natural joins) are commutative. E 1  E 2 = E 2  E 1 6. (a) Natural join operations are associative: ( E 1 E 2 ) E 3 = E 1 ( E 2 E 3 ) (b) Theta joins are associative in the following manner: ( E 1 1 E 2 ) 2  3 E 3 = E 1 1  3 ( E 2 2 E 3 ) where  2 involves attributes from only E 2 and E 3 . 14.9 Database System Concepts - 5 th Edition, Sep 1, 2006.

10. Pictorial Depiction of Equivalence Rules 14.10 Database System Concepts - 5 th Edition, Sep 1, 2006.

11. Equivalence Rules (Cont.) 7. The selection operation distributes over the theta join operation under the following two conditions: (a) When all the attributes in  0 involve only the attributes of one of the expressions ( E 1 ) being joined.  0 E 1  E 2 ) = ( 0 (E 1 ))  E 2 (b) When  1 involves only the attributes of E 1 and  2 involves only the attributes of E 2 .   1   E 1  E 2 ) = ( 1 (E 1 ))  (  (E 2 )) 14.11 Database System Concepts - 5 th Edition, Sep 1, 2006.

16. Multiple Transformations (Cont.) 14.16 Database System Concepts - 5 th Edition, Sep 1, 2006.

26. Join Order Optimization Algorithm procedure findbestplan( S ) if ( bestplan [ S ]. cost  ) return bestplan [ S ] // else bestplan [ S ] has not been computed earlier, compute it now if ( S contains only 1 relation) set bestplan [ S ]. plan and bestplan [ S ]. cost based on the best way of accessing S /* Using selections on S and indices on S */ else for each non-empty subset S 1 of S such that S 1  S P1= findbestplan( S 1) P2= findbestplan( S - S 1) A = best algorithm for joining results of P 1 and P 2 cost = P 1. cost + P 2. cost + cost of A if cost < bestplan [ S ]. cost bestplan [ S ]. cost = cost bestplan [ S ]. plan = “execute P 1. plan ; execute P 2. plan ; join results of P 1 and P 2 using A ” return bestplan [ S ] 14.26 Database System Concepts - 5 th Edition, Sep 1, 2006.

33. Statistics for Cost Estimation Database System Concepts 5 th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use

63. Extra Slides: Additional Optimization Techniques (see bibliographic notes) Database System Concepts 5 th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use

69. End of Chapter Database System Concepts 5 th Ed. ©Silberschatz, Korth and Sudarshan See www.db-book.com for conditions on re-use