1           Introduction of Relational algebra operations and query optimization

The internal representation of the query in the database is created as a query graph and query tree. Some of the alternative execution strategies are developed to retrieve the data from the database tables. The process of obtaining data from the execution strategy in query processing is known as query optimization (Dyer & Rogers, 2015). The query optimization is a complex process that uses alternative strategies based on different factors such as the presence of fragments, distribution of fragment under tables, speed of communication links, and local processing capabilities. Rational algebra is mainly a set of operations under the rational database model. The present work considers a database query under basic operations such as projection, selection, union, intersection, minus and joins operations.

2           Database description of Relational algebra operations and query optimization

In the present work relational algebra is used for the student database that displays names and courses of the students. In the query optimization process, a single query can be executed by considering several algorithms. The goal of the query optimization is to reduce the issues of database and obtain the system resources with faster results.

3           Database constraints of Relational algebra operations and query optimization

Consider the present case with the following student database for query optimization. The student database consists of roll number, name list, courses, semester, and gender of the students in a university (Cs. cornell. edu, 2019). The table 1 below provides student database with a display of courses and names of the students.

3.1        Database schema population with data
3.2        Queries

The goal of the work is query optimization that reduces the required system resources to fulfil the query. There are three methods of correct results that are mentioned below,

1.      Provider the user with fast results.

2.      Allow the system to serve the queries under the amount of time with the optimized queries.

3.      Query optimization for the ultimate reduction of issues and to allow the server of the database to run more efficiently with the low power consumption.  

3.2.1        Relational operations of Relational algebra operations and query optimization

There are two broad ways for query optimization,

1.      Analyze and transform the relational expressions to minimize the column counts and tuple the final query processes.

2.      Usage of algorithms to determine how tuples can be accessed from the data structure by using operations, hashing, data retrieval, and blocking access. 

3.2.2        Query of Relational algebra operations and query optimization

3.2.3        Query in relational algebra

The process uses the generation of minimal equivalent expressions and analyzes equivalent expression. The generation of equivalent expression for query work under the relational algebra. In order to optimize the query, it is important to convert the query into the equivalent forms and the rules used in the report are satisfied (Dyer & Rogers, 2015). 

3.3        Query optimization of Relational algebra operations and query optimization 

3.3.1        Query

The database system in the present work stores all the operating system files. The database is an integrated data collection and the concept is to store relevant information of students in the database. The whole system provides efficient storage and effective retrieval mechanisms. Query optimization is carried out with several important functions of the application. The query optimization provides a real experience of building a database solution for the administration of the school. The case study analysis help database teachers to imply effective relational algebra concepts (Tutorialspoint. com, 2020).

3.3.2        Query in relational algebra of Relational algebra operations and query optimization

The query in relational algebra is based on different functions. In the present work,9 relational algebra operations are used with the schema on a populated database application. The query optimization model use operations such as 

3.3.2.1       Selection of Relational algebra operations and query optimization

Selection is an operation in relational algebra that display all the subsets of tuples in a table and satisfies the conditions. In the relational algebra, the syntax of selection provides a horizontal partition of the database. For instance, in the student database, if the user wants to display details of all those students who opted for the BCA course, the following syntax of relational algebra can be used,

In some cases, the queries require a combination of selection and projection operations and there are two alternative expressions such as by using the sequence for selection and projection operations and by using rename operation for the generation of intermediate results. Another process is possible that is the selection of only male students of BCA course from the projection and database. In this case, the relational algebra expression becomes,

3.3.2.2       Union of Relational algebra operations and query optimization

The union operation is used to display a set of all tuples in two disciplines. Union operation is used for the display of students from semester 1 in BCA course.

3.3.2.3       Intersection of Relational algebra operations and query optimization

In the intersection section, a set of comment tuples is considered. Consider semester 1 as an operation for the MCA and BCA student selections.

3.3.2.4       Minus operation of Relational algebra operations and query optimization

In the minus operation set of all tuples in one dataset is selected that is not in the other database. For instance, in the present database, the information about the department is not present while the server of institute contains a database of each student with their department. Minus operation is used to find a list of all departments that were not in the database of ongoing projects.

3.3.2.5       Join of Relational algebra operations and query optimization

In the join operations, the combination of related tuples is collected from the database. In the join operation, the database is collected with the campus of the university.

3.3.3        Query tree of Relational algebra operations and query optimization

The query tree is developed in the present case for different name and titles of students in the database. The hash join operation is used as an operation between the course names of students and further process. the merge joins after the hash join is subdivided into two main categories through the pipelines of department name and year. the teachers and instructors are also kept in records of the database. The reliability of information is based on the accuracy of datasets in the database (Geeksforgeeks. org, 2020). 

4           Conclusion of Relational algebra operations and query optimization

Present work aimed to use database operations. The database considered in the present case is a student database of the institute that collect information about the name, roll number, subject, department, and gender of the students. Different operations can be carried out based on the requirement for the selection and operations of the data in the database.

5           References of Relational algebra operations and query optimization

Cs. cornell. edu. (2019). DATABASE MANAGEMENT SYSTEMS SOLUTIONS MANUAL. Retrieved from www.cs.cornell.edu: http://www.cs.cornell.edu/courses/cs432/2001fa/answers2ed-odd.pdf

Dyer, J. N., & Rogers, C. (2015). Mapping relation algebra operators into SQL queries: A database case study. Journal of Business Cases and Applications, 13(01), 01-10.

Geeksforgeeks. org. (2020). Query Optimization in Relational Algebra. Retrieved from www.geeksforgeeks.org: https://www.geeksforgeeks.org/query-optimization-in-relational-algebra/

Tutorialspoint. com. (2020). Relational Algebra for Query Optimization. Retrieved from www.tutorialspoint.com: https://www.tutorialspoint.com/distributed_dbms/distributed_dbms_relational_algebra_query_optimization.htm