Comparison Of The Roth-Vande Vate And Gale-Shapley Algorithm In The Placement Of New Employees Of PT. Indowebhost Creation

Feb 27, 2025 by ADMIN 123 views

Introduction

The placement of new employees in a company is a crucial process that requires careful consideration to ensure a good match between the company's needs and the desires of the employees. However, the traditional method of direct placement can be subjective and often leads to a mismatch between the two parties. To overcome this problem, the stable matching problem can be used, which aims to balance the company's needs and employee desires to produce a more just and effective decision for both parties.

The stable matching problem has been widely used in various industries, including education, healthcare, and business. Two of the most popular algorithms used to solve this problem are the Gale-Shapley algorithm and the Roth-Vande Vate algorithm. In this article, we will compare the two algorithms in the context of the placement of new employees at PT. Indowebhost Kreasi, a leading provider of web hosting services in Indonesia.

Background

The stable matching problem is a classic problem in computer science and economics that involves finding a stable matching between two sets of entities, such as employees and companies. The problem is defined as follows:

There are two sets of entities, E (employees) and C (companies).
Each employee has a preference list of companies, and each company has a preference list of employees.
The goal is to find a matching between the employees and companies that is stable, meaning that no employee and company can improve their match by switching to each other.

The Gale-Shapley algorithm and the Roth-Vande Vate algorithm are two of the most popular algorithms used to solve the stable matching problem. Both algorithms have been widely used in various industries, including education, healthcare, and business.

Gale-Shapley Algorithm

The Gale-Shapley algorithm is a popular algorithm used to solve the stable matching problem. The algorithm was first proposed by David Gale and Lloyd Shapley in 1962 and has since become a widely used algorithm in various industries.

The Gale-Shapley algorithm works as follows:

Each employee proposes to their most preferred company.
Each company receives the proposals from the employees and accepts the proposal from the employee who is their most preferred.
The employee who was rejected by the company proposes to their next most preferred company.
The process continues until all employees have been matched with a company.

The Gale-Shapley algorithm has a time complexity of O(N²), where N is the number of employees. The algorithm is simple to implement and has been widely used in various industries.

Roth-Vande Vate Algorithm

The Roth-Vande Vate algorithm is another popular algorithm used to solve the stable matching problem. The algorithm was first proposed by Alvin Roth and Marilda Sotomayor in 1990 and has since become a widely used algorithm in various industries.

The Roth-Vande Vate algorithm works as follows:

Each employee proposes to their most preferred company.
Each company receives the proposals from the employees and accepts the proposal from the employee who is their most preferred.
The employee who was rejected by the company proposes to their next most preferred company.
The process continues until all employees have been matched with a company.

The Roth-Vande Vate algorithm has a time complexity of O(N³), where N is the number of employees. The algorithm is more complex than the Gale-Shapley algorithm but has been shown to have better performance in certain contexts.

Comparison of Algorithm Complexity

The Roth-Vande Vate algorithm has a higher level of complexity than the Gale-Shapley algorithm, with a time complexity of O(N³) compared to O(N²) for the Gale-Shapley algorithm. This shows that the Roth-Vande Vate algorithm requires longer to complete the matching process, especially when the number of employees to be placed is more and more.

However, the Roth-Vande Vate algorithm has been shown to have better performance in certain contexts, such as when the number of employees is large and the preference lists are complex. In this study, the Roth-Vande Vate algorithm showed better performance in terms of completion time, with an average completion time of 43.4 MS compared to 70 MS for the Gale-Shapley algorithm.

Performance of Settlement Time

The performance of the two algorithms was evaluated in terms of settlement time, which is the time taken to complete the matching process. The results showed that the Roth-Vande Vate algorithm had a significantly better performance than the Gale-Shapley algorithm, with an average completion time of 43.4 MS compared to 70 MS.

This shows that the Roth-Vande Vate algorithm is more efficient in certain contexts, although it will require a deeper understanding of its use. The results also highlight the importance of considering the specific objectives and needs of the company when choosing an algorithm to solve the stable matching problem.

Conclusion

In conclusion, the selection of the right algorithm to solve the stable matching problem is crucial in the context of placement of new employees at PT. Indowebhost Kreasi. While the Gale-Shapley algorithm is simpler and has a lower complexity, the Roth-Vande Vate algorithm offers better speed and performance in terms of completion time.

Therefore, companies need to consider their specific objectives and needs when choosing an algorithm that will be used in the process of placing new employees. The results of this study highlight the importance of considering the performance of the algorithm in terms of settlement time, as well as its complexity and accuracy.

Recommendations

Based on the results of this study, the following recommendations are made:

The Roth-Vande Vate algorithm should be used in the context of placement of new employees at PT. Indowebhost Kreasi, due to its better performance in terms of completion time.
The Gale-Shapley algorithm should be used in contexts where the number of employees is small and the preference lists are simple.
Further research is needed to evaluate the performance of the two algorithms in different contexts and to develop more efficient algorithms for solving the stable matching problem.

Limitations

This study has several limitations that should be noted. Firstly, the study only evaluated the performance of the two algorithms in the context of placement of new employees at PT. Indowebhost Kreasi, and may not be generalizable to other contexts.

Secondly, the study only considered the performance of the two algorithms in terms of settlement time, and may not have captured other important factors such as accuracy and complexity.

Finally, the study only used a small sample size of employees and companies, and may not be representative of the larger population.

Future Research Directions

There are several future research directions that can be explored based on the results of this study. Firstly, further research is needed to evaluate the performance of the two algorithms in different contexts and to develop more efficient algorithms for solving the stable matching problem.

Secondly, the study only considered the performance of the two algorithms in terms of settlement time, and may not have captured other important factors such as accuracy and complexity. Further research is needed to evaluate the performance of the two algorithms in terms of these factors.

Finally, the study only used a small sample size of employees and companies, and may not be representative of the larger population. Further research is needed to evaluate the performance of the two algorithms in a larger sample size and to develop more generalizable results.

Conclusion

Q: What is the stable matching problem?

A: The stable matching problem is a classic problem in computer science and economics that involves finding a stable matching between two sets of entities, such as employees and companies. The problem is defined as follows:

There are two sets of entities, E (employees) and C (companies).
Each employee has a preference list of companies, and each company has a preference list of employees.
The goal is to find a matching between the employees and companies that is stable, meaning that no employee and company can improve their match by switching to each other.

Q: What is the Gale-Shapley algorithm?

A: The Gale-Shapley algorithm is a popular algorithm used to solve the stable matching problem. The algorithm was first proposed by David Gale and Lloyd Shapley in 1962 and has since become a widely used algorithm in various industries.

The Gale-Shapley algorithm works as follows:

Each employee proposes to their most preferred company.
Each company receives the proposals from the employees and accepts the proposal from the employee who is their most preferred.
The employee who was rejected by the company proposes to their next most preferred company.
The process continues until all employees have been matched with a company.

Q: What is the Roth-Vande Vate algorithm?

A: The Roth-Vande Vate algorithm is another popular algorithm used to solve the stable matching problem. The algorithm was first proposed by Alvin Roth and Marilda Sotomayor in 1990 and has since become a widely used algorithm in various industries.

The Roth-Vande Vate algorithm works as follows:

Each employee proposes to their most preferred company.
Each company receives the proposals from the employees and accepts the proposal from the employee who is their most preferred.
The employee who was rejected by the company proposes to their next most preferred company.
The process continues until all employees have been matched with a company.

Q: What are the advantages of the Roth-Vande Vate algorithm?

A: The Roth-Vande Vate algorithm has several advantages, including:

Better performance in terms of completion time, with an average completion time of 43.4 MS compared to 70 MS for the Gale-Shapley algorithm.
More efficient in certain contexts, although it will require a deeper understanding of its use.
Can handle complex preference lists and large numbers of employees.

Q: What are the disadvantages of the Roth-Vande Vate algorithm?

A: The Roth-Vande Vate algorithm has several disadvantages, including:

Higher level of complexity, with a time complexity of O(N³) compared to O(N²) for the Gale-Shapley algorithm.
Requires longer to complete the matching process, especially when the number of employees to be placed is more and more.
May not be suitable for small-scale applications or applications with simple preference lists.

Q: When should I use the Gale-Shapley algorithm?

A: You should use the Gale-Shapley algorithm in the following situations:

When the number of employees is small and the preference lists are simple.
When the completion time is not a critical factor.
When the complexity of the algorithm is not a concern.

Q: When should I use the Roth-Vande Vate algorithm?

A: You should use the Roth-Vande Vate algorithm in the following situations:

When the number of employees is large and the preference lists are complex.
When the completion time is a critical factor.
When the complexity of the algorithm is not a concern.

Q: How do I choose between the Gale-Shapley algorithm and the Roth-Vande Vate algorithm?

A: You should choose between the Gale-Shapley algorithm and the Roth-Vande Vate algorithm based on the specific needs of your application. Consider the following factors:

The number of employees and the complexity of the preference lists.
The importance of completion time and the complexity of the algorithm.
The specific objectives and needs of your application.

Q: Can I use both algorithms in the same application?

A: Yes, you can use both algorithms in the same application. However, you should consider the following factors:

The complexity of the algorithm and the completion time.
The specific objectives and needs of your application.
The trade-offs between the two algorithms.

Q: What are the future research directions for the stable matching problem?

A: There are several future research directions for the stable matching problem, including:

Developing more efficient algorithms for solving the stable matching problem.
Evaluating the performance of the two algorithms in different contexts and developing more generalizable results.
Developing more complex and realistic models of the stable matching problem.

Q: What are the practical applications of the stable matching problem?

A: The stable matching problem has several practical applications, including:

Placement of new employees in companies.
Matching of students with universities.
Matching of patients with hospitals.
Matching of customers with products.

Q: What are the limitations of the stable matching problem?

A: The stable matching problem has several limitations, including:

The assumption of stable matching may not always hold in real-world applications.
The complexity of the algorithm and the completion time may be a concern in certain applications.
The model may not capture the complexity of real-world applications.

Q: What are the future research directions for the Gale-Shapley algorithm?

A: There are several future research directions for the Gale-Shapley algorithm, including:

Developing more efficient versions of the algorithm.
Evaluating the performance of the algorithm in different contexts and developing more generalizable results.
Developing more complex and realistic models of the stable matching problem.

Q: What are the future research directions for the Roth-Vande Vate algorithm?

A: There are several future research directions for the Roth-Vande Vate algorithm, including:

Developing more efficient versions of the algorithm.
Evaluating the performance of the algorithm in different contexts and developing more generalizable results.
Developing more complex and realistic models of the stable matching problem.

Q: What are the practical applications of the Gale-Shapley algorithm?

A: The Gale-Shapley algorithm has several practical applications, including:

Placement of new employees in companies.
Matching of students with universities.
Matching of patients with hospitals.
Matching of customers with products.

Q: What are the practical applications of the Roth-Vande Vate algorithm?

A: The Roth-Vande Vate algorithm has several practical applications, including:

Placement of new employees in companies.
Matching of students with universities.
Matching of patients with hospitals.
Matching of customers with products.

Q: What are the limitations of the Gale-Shapley algorithm?

A: The Gale-Shapley algorithm has several limitations, including:

The assumption of stable matching may not always hold in real-world applications.
The complexity of the algorithm and the completion time may be a concern in certain applications.
The model may not capture the complexity of real-world applications.

Q: What are the limitations of the Roth-Vande Vate algorithm?

A: The Roth-Vande Vate algorithm has several limitations, including:

The assumption of stable matching may not always hold in real-world applications.
The complexity of the algorithm and the completion time may be a concern in certain applications.
The model may not capture the complexity of real-world applications.