1. 16.4 Estimating the Cost of Operations Project GuidePrepared By Dr. T. Y. LinAkshay Shenoy Computer Science Dept San Jose State University

2. Introduction Possible Physical Plan Estimating Sizes of Intermediate Relations Estimating the Size of a Projection Estimating the Size of a Selection Estimating the Size of a Join Natural Joins With Multiple Join Attributes Joins of Many Relations Estimating Sizes of Other Operations

3. Physical Plan For each physical plan select An order and grouping for associative-and- commutative operations like joins, unions. An Algorithm for each operator in the logical plan. eg: whether nested loop join or hash join to be used Additional operators that are needed for the physical plan but that were not present explicitly in the logical plan. eg: scanning, sorting The way in which arguments are passed from one operator to the next.

4. Estimating Sizes of Intermediate Relations Rules for estimating the number of tuples in an intermediate relation: 1.Give accurate estimates 2.Are easy to compute 3.Are logically consistent Objective of estimation is to select best physical plan with least cost.

5. Estimating the Size of a Projection The projection is different from the other operators, in that the size of the result is computable. Since a projection produces a result tuple for every argument tuple, the only change in the output size is the change in the lengths of the tuples.

6. Estimating the Size of a Selection(1) Let,,where A is an attribute of R and C is a constant. Then we recommend as an estimate: T(S) =T(R)/V(R,A) The rule above surely holds if all values of attribute A occur equally often in the database.

7. Estimating the Size of a Selection(2) If,then our estimate for T(s) is: T(S) = T(R)/3 We may use T(S)=T(R)(V(R,a) -1 )/ V(R,a) as an estimate. When the selection condition C is the And of several equalities and inequalities, we can treat the selection as a cascade of simple selections, each of which checks for one of the conditions.

8. Estimating the Size of a Selection(3) A less simple, but possibly more accurate estimate of the size of is to assume that C1 and of which satisfy C2, we would estimate the number of tuples in S as In explanation, is the fraction of tuples that do not satisfy C1, and is the fraction that do not satisfy C2. The product of these numbers is the fraction of R’s tuples that are not in S, and 1 minus this product is the fraction that are in S.

9. Estimating the Size of a Join two simplifying assumptions: 1. Containment of Value Sets If R and S are two relations with attribute Y and V(R,Y)<=V(S,Y) then every Y-value of R will be a Y-value of S. 2. Preservation of Value Sets Join a relation R with another relation S with attribute A in R and not in S then all distinct values of A are preserved and not lost.V(S R,A) = V(R,A) Under these assumptions, we estimate T(R S) = T(R)T(S)/max(V(R,Y), V(S, Y))

10. Natural Joins With Multiple Join Attributes Of the T(R),T(S) pairs of tuples from R and S, the expected number of pairs that match in both y1 and y2 is: T(R)T(S)/max(V(R,y1), V(S,y1)) max(V(R, y2), V(S, y2)) In general, the following rule can be used to estimate the size of a natural join when there are any number of attributes shared between the two relations. The estimate of the size of R S is computed by multiplying T(R) by T(S) and dividing by the largest of V(R,y) and V(S,y) for each attribute y that is common to R and S.

11. Joins of Many Relations(1) rule for estimating the size of any join Start with the product of the number of tuples in each relation. Then, for each attribute A appearing at least twice, divide by all but the least of V(R,A)’s. We can estimate the number of values that will remain for attribute A after the join. By the preservation-of-value-sets assumption, it is the least of these V(R,A)’s.

12. Joins of Many Relations(2) Based on the two assumptions-containment and preservation of value sets: No matter how we group and order the terms in a natural join of n relations, the estimation of rules, applied to each join individually, yield the same estimate for the size of the result. Moreover, this estimate is the same that we get if we apply the rule for the join of all n relations as a whole.

13. Estimating Sizes for Other Operations Union: the average of the sum and the larger. Intersection: approach1: take the average of the extremes, which is the half the smaller. approach2: intersection is an extreme case of the natural join, use the formula T(R S) = T(R)T(S)/max(V(R,Y), V(S, Y))

14. Estimating Sizes for Other Operations Difference: T(R)-(1/2)*T(S) Duplicate Elimination: take the smaller of (1/2)*T(R) and the product of all the V(R, )’s. Grouping and Aggregation: upper-bound the number of groups by a product of V(R,A)’s, here attribute A ranges over only the grouping attributes of L. An estimate is the smaller of (1/2)*T(R) and this product.

15. THANK YOU