Exercise 15.7 Consider the following relational schema and SQL query. The schema captures...

Exercise 15.7 Consider the following relational schema and SQL query. The schema captures information about employees, departments, and company finances (organized on a per department basis).

 Emp(eid: integer, did: integer, sal: integer, hobby: char(20)) Dept(did: integer, dname: char(20), floor: integer, phone: char(10)) Finance(did: integer, budget: real, sales: real, expenses: real)

Consider the following query:

 SELECT D.dname, F.budget FROM Emp E, Dept D, Finance F WHERE E.did=D.did AND D.did=F.did AND D.floor=1       AND E.sal ≥ 59000 AND E.hobby = ‘yodeling’

1. Identify a relational algebra tree (or a relational algebra expression if you prefer) that reflects the order of operations a decent query optimizer would choose.

2. List the join orders (i.e., orders in which pairs of relations can be joined to compute the query result) that a relational query optimizer will consider. (Assume that the optimizer follows the heuristic of never considering plans that require the computation of cross-products.) Briefly explain how you arrived at your list.

3. Suppose that the following additional information is available: Unclustered B+ tree indexes exist on Emp.did, Emp.sal, Dept.floor, Dept.did, and Finance.did. The system’s statistics indicate that employee salaries range from 10,000 to 60,000, employees enjoy 200 different hobbies, and the company owns two floors in the building. There are a total of 50,000 employees and 5,000 departments (each with corresponding financial information) in the database. The DBMS used by the company has just one join method available, index nested loops.

(a) For each of the query’s base relations (Emp, Dept, and Finance) estimate the number of tuples that would be initially selected from that relation if all of the non-join predicates on that relation were applied to it before any join processing begins.

(b) Given your answer to the preceding question, which of the join orders considered by the optimizer has the lowest estimated cost?