Chapter 16, Problem 6PE

Explanation of Solution

To estimate the size of the r1 |><| r2 |><| r3:

• Consider the following three relations,
  • r1(A,B,C)
  • r2(C,D,E)
  • r3(E,F)
• The above relations r1, r2, and r3 having the primary keys “A”, “C” and “E” respectively.
• In relational algebra, the associative and communicative properties are exhibited using joins.
• Hence, joining thee relations produce the same result.
• To get the two natural joins, calculate the average number of records that would be joined with each record of the second relation for both the joins.
• The average number of records of relation r2 will join with each record of relation r1 is calculated as follows,

$\begin{array}{ccc}\text{The}\text{average}\text{number}\text{of}\text{records}& =& \frac{\text{records}\text{in}\text{r2}}{\text{V(C,}\text{r2)}}\\ & =& \frac{1500}{1100}\\ & =& \frac{15}{11}\text{records}\end{array}$

• The result of first join will have the following number of records,

$\begin{array}{cc}\text{The}\text{number}\text{of}\text{records}& =\frac{15}{11}\times 1000\\ & =\frac{15000}{11}\end{array}$

• The number of record obtained from the above step will be joined with relation r3 and calculate the size at the same time