Question

Develop cost functions for an algorithm that consists of two SELECTs, a JOIN, and a final PROJECT, in terms of the cost functions for the individual operations.

Short answer

The total cost function for an algorithm constituted by two SELECT operations, a JOIN operation, and a PROJECT operation, given the individual operation costs are denoted by \( S \) , \( J \), and \( P \) respectively, is 'Total Cost' = 2*\( S \) + \( J \) + \( P \)

Step-by-step solution

Address the Cost of SELECT

SELECT operation is used to fetch data from a database. Let's denote the cost of a SELECT operation as \( S \). It should be noted that we have two SELECT operations in this exercise

Address Cost of JOIN

JOIN operation is used to combine rows from two or more tables. This operation is typically resource-intensive. Let's denote the cost of the JOIN operation as \( J \)

Address Cost of PROJECT

PROJECT operation is used to select the necessary fields without selecting all fields. Let's denote the cost of the PROJECT operation as \( P \)

Formulate Aggregate Cost Function

Now, assuming that these operations will be performed one after the other, and considering the number of each operation, the cost function for the entire procedure can be formulated as follows: 'Total Cost' = 2*\( S \) + \( J \) +\( P \)

Key concepts

SELECT Operation

The SELECT operation in database management is crucial for retrieving fixed sets of data based on specific conditions. When thinking about the SELECT operation, you can imagine it as asking the database to provide only the pieces of information you're interested in.

To perform a SELECT, a query is executed, and this operation fetches data from one or more tables, as determined by the criteria specified in the query. For example, if you need to find all the students with a grade above 85, you would write a SELECT operation to fetch only those results.

In cost terms, each SELECT operation has its own computational expense, which we'll denote as \( S \). The complexity of this cost can depend on factors such as the size of the data set being searched and the efficiency of the indexes used in the database. In our scenario, there are two SELECT operations, indicating that the computational cost will add up to \( 2S \) when both are performed.

JOIN Operation

The JOIN operation is another fundamental database function used to combine rows from two or more tables based on a related column. Consider JOIN as the database's way of building connections between different sets of data.

For instance, think of having separate tables for 'Students' and 'Courses,' and you want to create a list of students with their respective enrolled courses. A JOIN operation would help in merging these tables to get the desired information.

This operation can become quite resource-intensive because it often involves scanning through large quantities of data to find related entries. In terms of cost, we assign this operation the label \( J \). The cost associated with performing a JOIN can vary greatly based on how many rows are being compared and the complexity of the joining conditions. Therefore, JOIN typically stands as one of the heaviest operations in terms of computational load.

PROJECT Operation

The PROJECT operation is used to limit the results to only the columns specified, effectively reducing the number of fields in the output. This operation is akin to picking only the necessary parts of a record.

Imagine you have a full report with twenty different data fields, but you're only interested in the first name and last name. A PROJECT operation would help in filtering out just those fields, giving you a cleaner, simpler dataset.

When we consider cost, the PROJECT operation is often less expensive than JOIN, as it merely focuses on selecting the needed columns. We'll denote its cost as \( P \). The exact cost might vary depending on the number of columns to be retrieved and the size of the data set, but it's usually efficient and quick compared to other operations. The PROJECT operation, in combination with SELECT and JOIN, helps tailor the final output to exactly what is needed without extra data cluttering the result.