## 4 Experimental Results and Analysis
### Findings and Discussion  
The circuit-partitioning optimization algorithm based on clustering and improved tabu search proposed in this study demonstrates certain advantages, particularly in reducing cut edges and optimizing load balancing. By abstracting the circuit as an undirected graph and combining clustering with the collaborative optimization of improved tabu search, we are able to effectively reduce the number of cut edges and improve the quality of partitioning. The experimental results show that the proposed algorithm performs better than traditional algorithms, such as Metis and KL, especially when handling large-scale circuits. Compared to Metis, the proposed algorithm offers several key improvements. Metis typically requires re-optimization after each uncoarsing step, leading to increased computational complexity and time consumption. In contrast, our algorithm performs further optimization directly after uncoarsing, eliminating the need for repeated optimization steps. This approach reduces the time overhead associated with multiple optimization iterations and enhances overall computational efficiency. Moreover, during the tabu search phase, our algorithm utilizes bucket data structures and hash tables, which significantly speed up the computation process. While Metis may require considerable time for the initial partitioning, our algorithm, thanks to its optimized data structures and design, can complete the tabu search phase more quickly. This advantage becomes especially apparent when handling large-scale circuits, where our approach outperforms traditional methods in both execution time and computational load. The improved tabu search algorithm, through its innovative perturbation mechanism and high-quality neighborhood search, is able to converge to better solutions relatively  
Figure 8: Comparison of ratios for different k values. This graph shows the performance comparison of the proposed algorithm and other algorithms in optimizing the minimum cut edges across different \(k\) values. A lower ratio indicates better performance of the proposed algorithm in the test cases. quickly, demonstrating reasonable single-thread optimization capabilities. Although the algorithm is executed in a single-thread environment, its efficient neighborhood search and perturbation strategy allow it to find better solutions in a relatively short time, exhibiting a reasonable level of computational efficiency. In a single-threaded environment, the algorithm effectively shortens computation time, and as the scale of the circuit increases, its computational efficiency remains within a reasonable range, showing a certain degree of scalability. In particular, when dealing with large-scale circuits, the tabu search algorithm refines the initial partitioning results, further reducing the number of cut edges while maintaining a good load balance. Even when faced with circuits containing a large number of nodes and edges, the algorithm remains stable and effective. While this is a single-threaded algorithm, its rapid convergence and efficient search process allow it to handle larger-scale circuits, demonstrating strong adaptability in practical applications. When compared with Metis and KL algorithms, our algorithm outperforms them in reducing the number of cut edges, and even as the circuit scale increases, the optimization results remain stable and the computational time increases insignificantly. This indicates that the algorithm exhibits strong scalability in a single-threaded environment and can handle circuit partitioning tasks of varying scales and complexities. However, when dealing with extremely complex and irregular circuit structures, the initial partition may not always find the optimal solution, limiting the optimization potential of the subsequent refinement process. Future research could further optimize the perturbation mechanism and neighborhood search strategy of the tabu search algorithm to enhance its accuracy and stability.