# Dynamic Workload Management System in the Public Sector: A Comparative Analysis
## 5 Discussion  
### Time Complexity  
The efficiency and scalability of algorithms in machine learning are crucial. Understanding the time complexity of various machine learning algorithms is critical in choosing the most appropriate for any task. We investigate the time complexity of all seven algorithms. The time complexity of Linear Regression is n, where n is the number of data points. Simple mathematical calculations make them highly efficient, especially for large datasets. Neural networks are known for their adaptability to complex tasks. Still, the time complexity of training neural networks depends on factors such as architecture and optimization algorithms. At the same time, it ranges from \(\mathcal{O}(n*m*k)\), where '\(n\)' is the number of samples, '\(m\)' is the number of layers, and '\(k\)' is the number of iterations. ANFIS combines fuzzy logic and neural networks to model complex relationships. At the same time, its time complexity is analogous to neural networks, standing at \(\mathcal{O}(n*m*k)\). '\(n\)' represents data points, '\(m\)' denotes the number of rules, and '\(k\)' signifies the number of iterations. Bagging involves the training of multiple decision trees in parallel and introduces time complexity of \(\mathcal{O}(m*n*\log(n))\), where '\(m\)' stands for features, and '\(n\)' for data points.  
The time complexity for Bagging is shown by \(\mathcal{O}(m*n*\log(n))\), where'm' stands for features, and 'n' for data points, while the parallelization introduced further enhances the efficiency of this ensemble method.  
XGBoost is close enough to the time complexity of GBM at approximately \(\mathcal{O}(n*m*k)\). In addition, it leverages data pruning techniques and parallel processing, giving credit to its efficiency and scalability. SVMs, on the other hand, while effective in many scenarios, exhibit variable time complexities. They range from \(\mathcal{O}(n^{2}*m)\) to \(\mathcal{O}(n^{3}*m)\)  
Figure 14: Load Control based on CF produced from algorithms. (**a**) Load Control: ANFIS; (**b**) Load Control: Regression Analysis; (**c**) Load Control: ANN; (**d**) Load Control: Gradient Boosting Machine; (**e**) Load Control: Bagged Decision Trees; (**f**) Load Control: Support Vector Machines; (**g**) Load Control: XGBoost.  
contingent on the kernel used. Here, '_n_' stands for data points, and '_m_' for features. SVMs require substantial hardware processing for extensive datasets and high-dimensional feature spaces.  
While ANFIS incurs a substantial computational expense, it remains a prominent choice across various applications owing to its proficiency in acquiring and depicting intricate non-linear associations.  
As shown in Table 14, the comparative analysis of CPU time and memory usage highlights significant differences across the algorithms, reflecting their computational efficiency and resource demands. Linear Regression is the most lightweight algorithm, with minimal CPU time (10-30 ms) and memory usage (5-15 MB), making it suitable for simple, linear datasets. On the other hand, Artificial Neural Networks (ANNs) and Adaptive Neuro-Fuzzy Inference System (ANFIS) demand higher resources, with CPU times of 120-180 ms and 180-220 ms and memory usage of 30-50 MB and 40-60 MB, respectively, due to their ability to model complex, non-linear relationships. Ensemble methods, such as Gradient Boosting Machine (GBM) and Bagged Decision Trees, exhibit moderate resource demands, with CPU times ranging from 140 to 200 ms and memory usage from 30 to 50 MB, balancing complexity and efficiency. Support Vector Machine (SVM) and XGBoost, known for their robust performance on complex datasets, show the highest CPU times (200-260 ms and 200-240 ms, respectively) and memory usage (50-60 MB and 40-55 MB), reflecting their computational intensity. This analysis underscores the trade-off between computational resources and predictive power, emphasizing the importance of selecting algorithms that align with the specific requirements of the dataset and application.