1. Query Compiler By:Payal Gupta Roll No:106(225) Professor :Tsau Young Lin

2. Pushing Selections It is, replacing the left side of one of the rules by its right side. In pushing selections we first a selection as far up the tree as it would go, and then push the selections down all possible branches.

3. Let’s take an example: S t a r s I n ( t i t l e, year, starName) Movie(title, year, length, incolor, studioName, producerC#) Define view MoviesOf 1996 by: CREATE VIEW MoviesOfl996 AS SELECT * FROM Movie,WHERE year = 1996;

4. "which stars worked for which studios in 1996?“ can be given by a SQL Query: SELECT starName, studioName FROM MoviesOfl996 NATURAL JOIN StarsIn;

5. ΠstarName,studioName O Year=1996 StarsIn Movie Logical query plan constructed from definition of a query and view

6. ΠstarName,studioName O Year=1996 StarsIn Movie Year=1996 O Improving the query plan by moving selections up and down the tree

7. "pushing" projections really involves introducing a new projection somewhere below an existing projection. projection keeps the number of tuples the same and only reduces the length of tuples. To describe the transformations of extended projection Consider a term E + x on the list for a projection, where E is an attribute or an expression involving attributes and constants and x is an output attribute. Laws Involving Projection

8. Example Let R(a, b, c) and S(c, d, e) be two relations. Consider the expression x,+,,,, b+y(R w S). The input attributes of the projection are a,b, and e, and c is the only join attribute. We may apply the law for pushing projections below joins to get the equivalent expression: Πa+e->x,b->y(Πa,b,c(R) Πc,e(S)) Eliminating this projection and getting a third equivalent expression:Πa+e->x, b->y( R Πc,e(S))

9. In addition, we can perform a projection entirely before a bag union. That is: ΠL(R UB S)= ΠL(R) )UB ΠL(S)

10. Laws About Joins and Products laws that follow directly from the definition of the join: R c S = c( R * S) R S = ΠL( c ( R * S) ), where C is the condition that equates each pair of attributes from R and S with the same name. and L is a list that includes one attribute from each equated pair and all the other attributes of R and S. We identify a product followed by a selection as a join of some kind. O O

11. Laws Involving Duplicate Elimination The operator δ which eliminates duplicates from a bag can be pushed through many but not all operators. In general, moving a δ down the tree reduces the size of intermediate relations and may therefore beneficial. Moreover, sometimes we can move δ to a position where it can be eliminated altogether,because it is applied to a relation that is known not to possess duplicates.

12. δ (R)=R if R has no duplicates. Important cases of such a relation R include: a) A stored relation with a declared primary key, and b) A relation that is the result of a γ operation, since grouping creates a relation with no duplicates.

13. Several laws that "push" δ through other operators are: δ (R*S) =δ(R) * δ(S) δ (R S)=δ(R) δ(S) δ (R c S)=δ(R) c δ(S) δ ( c (R))= c (δ(R)) We can also move the δ to either or both of the arguments of an intersection: δ (R ∩ B S) = δ(R) ∩ B S = R ∩ B δ (S) = δ(R) ∩ B δ (S) OO

14. Laws Involving Grouping and Aggregation When we consider the operator γ, we find that the applicability of many transformations depends on the details of the aggregate operators used. Thus we cannot state laws in the generality that we used for the other operators. One exception is that a γ absorbs a δ. Precisely: δ(γ L (R))=γ L (R)

15. let us call an operator γ duplicate-impervious if the only aggregations in L are MIN and/or MAX then: γ L(R) = γ L (δ(R)) provided γL is duplicate-impervious.

16. Example Suppose we have the relations MovieStar(name, addr, gender, birthdate) StarsIn(movieTitle, movieyear, starname) and we want to know for each year the birthdate of the youngest star to appear in a movie that year. We can express this query as: SELECT movieyear, MAX(birth date) FROM MovieStar, StarsIn WHERE name = starName GROUP BY movieyear;

17. γ movieYear, MAX ( birthdate ) name = starName MovieStar StarsIn Initial logical query plan for the query O

18. Some transformations that we can apply to Fig are 1. Combine the selection and product into an equijoin. 2.Generate a δ below the γ, since the γ is duplicate- impervious. 3. Generate a Π between the γ and the introduced δ to project onto movie-Year and birthdate, the only attributes relevant to the γ

19. γ movieYear, MAX ( birthdate ) Π movieYear, birthdate δ name = starName MovieStar StarsIn Another query plan for the query

20. γ movieYear, MAX ( birthdate ) Π movieYear, birthdate name = starName δ Π birthdate,name Π movieYear,starname MovieStar StarsIn third query plan for Example

21. Thank You