Write A 1000-Word Essay, Reproducing The Corresponding Algor

Write a 1000 word essay reproducing the corresponding algorithm or definition

Write a 1000 word essay, reproducing the corresponding algorithm or definition

This exam consists of three parts. Part 1 involves writing SQL queries and creating table statements based on a given schema. Part 2 requires composing a detailed essay about the attribute closure algorithm, including its reproduction, line-by-line description, an example with specific attributes, and applications. Part 3 asks for a personalized, in-depth essay (~1000 words) on the functional dependencies closure, reproducing the algorithm or definition, describing it line by line, and explaining its logic and applications, tailored to a topic associated with your name.

Paper For Above instruction

Part 1: SQL Queries and Table Creation

Given the schema:

  • employee (employee-name, street, city)
  • works (employee-name, company-name, salary)
  • company (company-name, city)
  • manages (employee-name, manager-name)

which allows multiple jobs per person and multiple cities per company, the following SQL queries are formulated:

  1. List of employee names working for Google:
  2. SELECT DISTINCT e.employee-name

    FROM employee e

    JOIN works w ON e.employee-name = w.employee-name

    WHERE w.company-name = 'Google';

  3. Names and residence cities of employees working for Google:
  4. SELECT e.employee-name, e.city

    FROM employee e

    JOIN works w ON e.employee-name = w.employee-name

    WHERE w.company-name = 'Google';

  5. Names, streets, and cities for employees working for Google earning over $250,000:
  6. SELECT e.employee-name, e.street, e.city

    FROM employee e

    JOIN works w ON e.employee-name = w.employee-name

    WHERE w.company-name = 'Google' AND w.salary > 250000;

  7. Employees living in the same city as their company:
  8. SELECT e.employee-name

    FROM employee e

    JOIN company c ON e.city = c.city

    JOIN works w ON e.employee-name = w.employee-name

    WHERE c.company-name = w.company-name;

  9. Employees living on the same street and in the same city as their managers:
  10. SELECT e.employee-name

    FROM employee e

    JOIN manages m ON e.employee-name = m.employee-name

    JOIN employee mng ON m.manager-name = mng.employee-name

    WHERE e.street = mng.street AND e.city = mng.city;

  11. Employees who do not work for Google:
  12. SELECT e.employee-name

    FROM employee e

    JOIN works w ON e.employee-name = w.employee-name

    WHERE w.company-name 'Google' OR w.company-name IS NULL;

  13. Create statement for 'works' table including keys:
  14. CREATE TABLE works (

    employee-name VARCHAR(50),

    company-name VARCHAR(50),

    salary DECIMAL(10,2),

    PRIMARY KEY (employee-name, company-name),

    FOREIGN KEY (employee-name) REFERENCES employee(employee-name),

    FOREIGN KEY (company-name) REFERENCES company(company-name)

    );

  15. Part 2: Attribute Closure Algorithm
  16. The attribute closure algorithm is fundamental in relational database theory, particularly in identifying candidate keys. It computes the set of attributes functionally determined by a given set by iteratively applying functional dependencies until no new attributes can be added. The motivation lies in optimizing database design, analyzing normalization, and ensuring data integrity.
  17. The algorithm begins with an initial attribute set, say X, and then adds attributes C whenever a dependency C -> D exists and C is a subset of the current set. The process repeats until no new attributes can be added, signifying the attribute closure of X, denoted as (X)+, has been obtained. The attribute closure is instrumental in identifying candidate keys, as attributes whose closure covers all attributes of the relation are potential keys.
  18. For example, considering relation R with attributes {A, B, C, D, E} and functional dependencies:
  • B -> A
  • C -> A
  • DE -> AC
  • E -> B

The process for computing, say, (C,D)+ involves starting with {C,D} and applying dependencies iteratively:

  1. Initialize (C,D)+ = {C,D}.
  2. Since C -> A, add A: (C,D)+ = {A, C, D}.
  3. As D has no direct dependencies, check DE -> AC: with D and E, but E is not in current set, so skip.
  4. If E were in set, then E -> B, which when combined with previous, adds B and possibly more.
  5. Repeat until no new attributes are added, resulting in {(C,D)+ = {A, B, C, D, E}} if possible, or partial depending on dependencies.

Finding candidate keys involves checking minimal attribute sets whose closures contain all attributes; for instance, {(E, C)} if (E,C)+ = {A, B, C, D, E}.

Applications of the attribute closure algorithm extend beyond candidate keys, including normalization, redundancy elimination, and anomaly detection, making it a cornerstone in relational database design.

Part 3: Personalized Essay on Functional Dependencies Closure Based on the Name 'Alfifi'

Assuming the personalized topic is "Alfifi Functional Dependencies Closure," this essay explores the concept of functional dependencies (FDs), their closure, and the algorithms used to compute closure sets. Functional dependencies are constraints that express relationships between attributes in a relational database. They specify how the value of one set of attributes determines the value of another.

The closure of FDs, denoted as F+, is the set of all functional dependencies implied by a given set F. Computing F+ involves applying Armstrong's axioms—reflexivity, augmentation, and transitivity—to derive all dependencies logically implied by the base set F. This process is fundamental in normalization, as it allows database designers to understand all constraints that hold in their schema and to identify keys and redundancies.

Reproducing the algorithm for computing F+ involves initializing the set with the given dependencies and then applying Armstrong's axioms repeatedly in a systematic manner until no new dependencies are added. The algorithm's complexity depends on the size of the attribute set and the initial dependencies, but it is generally polynomial in the size of the schema.

The step-by-step logic includes starting with the initial set of dependencies, expanding via reflexivity (if X then X), augmentation (if X -> Y, then XZ -> YZ), and transitivity (if X -> Y and Y -> Z, then X -> Z). These rules enable the derivation of all implied dependencies. For practical purposes, algorithms often employ algorithms that systematically explore these inferences without redundant checks.

Understanding F+ has core applications—such as detecting redundant dependencies, verifying normalization forms, and designing minimal covers—underscoring its importance in robust database schema design. For instance, to verify if a set of attributes forms a candidate key, one can compute their closure under F to check if the closure includes all attributes, ensuring uniqueness.

In conclusion, the closure of functional dependencies provides a comprehensive view of the implied constraints within a relational schema, serving as a vital tool for database normalization and integrity assurance. Its systematic computation via algorithmic methods ensures that designers can confidently normalize their schemas, eliminate redundancies, and enforce data integrity efficiently.

References

  • Abiteboul, S., Hull, R., & Vianu, V. (1995). Foundations of Databases. Addison-Wesley.

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