## 4 Experimental Results and Analysis
### Analysis of the Two-Way Partitioning Results  
#### 4.1.1 Analysis of Minimum Edge Cut Results  
The proposed algorithm is compared with the well-known partitioning tool Metis, the classic KL algorithm, and a genetic algorithm. Metis is from Karypis Lab, the KL algorithm is \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline \(V_{limit}\) & Coarsening threshold & 200 \\ \(LR\) & Clustering weight lower bound threshold & \(V/k\times(1-\beta)\) \\ \(\alpha\) & Tabu list length factor & 0.1 \\ \(P_{str}\) & Perturbation strength & 0.02 \(\times\)\(V\) \\ \(\gamma\) & Number of iterations before perturbation & 0.01 \(\times\)\(V\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter settings for the proposed algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Circuit** & **Number of Vertices** & **Number of Edges** \\ \hline c432 & 160 & 576 \\ c499 & 202 & 1016 \\ c880 & 383 & 1238 \\ c1335 & 546 & 2200 \\ c1908 & 880 & 3118 \\ s1423 & 731 & 6166 \\ s5378 & 2958 & 23,184 \\ s9234 & 5808 & 38,053 \\ s13207 & 8589 & 231,525 \\ s15850 & 10,306 & 174,787 \\ s35932 & 17,793 & 2,703,410 \\ s38417 & 23,815 & 1,159,273 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test circuits and their vertex and edge counts. from reference [9], and the genetic algorithm is from reference [13]. To improve the validity of the experiments, each of the above algorithms was run 30 times, and the minimum and average cut sizes (Min and Avg) were recorded. All experiments were conducted under the condition that the balance factor \(\beta\) was controlled within 0.2. The results are shown in Table 3.  
Figure 7 shows the comparison of the minimum cut edges between the proposed algorithm and other algorithms. The experimental results demonstrate that the proposed algorithm performs excellently in circuit partitioning, overall outperforming METIS, KL algorithms, and the genetic algorithm. By comparing the minimum edge cuts (Min) and average edge cuts (Avg) of various circuits, we found that the proposed algorithm achieves optimization in most cases. Specifically, for the minimum edge cuts (Min), the proposed algorithm reaches 0.78-1.01 times that of METIS, with an average of 0.92 times; compared to KL, reaches 0.52-0.67 times, with an average of 0.62 times. As shown in Figure 7, compared to other algorithms, the ratio of the minimum cut edges is below 1 in most cases, indicating an improvement in the minimum edge cuts. However, the proposed algorithm shows weaker \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Circuit**} & \multicolumn{2}{c}{**Metis**} & \multicolumn{2}{c}{**KL [9]**} & \multicolumn{2}{c}{**Genetic [13]**} & \multicolumn{2}{c}{**Proposed**} \\ \cline{2-9}  & **Min** & **Avg** & **Min** & **Avg** & **Min** & **Avg** & **Min** & **Avg** \\ \hline c432 & 48 & 48 & 72 & 75 & 52 & 55 & 47 & 51 \\ c499 & 57 & 57 & 85 & 93 & 66 & 68 & 48 & 50 \\ c880 & 46 & 46 & 69 & 78 & 63 & 77 & 43 & 45 \\ c1335 & 60 & 60 & 90 & 112 & 79 & 83 & 47 & 53 \\ c1908 & 69 & 69 & 104 & 121 & 45 & 53 & 58 & 60 \\ s1423 & 250 & 250 & 375 & 391 & 277 & 289 & 234 & 241 \\ s5378 & 356 & 356 & 534 & 542 & 412 & 451 & 352 & 354 \\ s9234 & 491 & 491 & 736 & 756 & 512 & 564 & 496 & 524 \\ s13207 & 1429 & 1429 & 1484 & 1567 & 1797 & 1923 & 1348 & 1426 \\ s15850 & 1468 & 1468 & 2202 & 2347 & 1436 & 1613 & 1358 & 1436 \\ s35932 & 7232 & 7232 & 7467 & 7871 & 7119 & 7324 & 6893 & 6980 \\ s38417 & 3286 & 3286 & 4929 & 5102 & 3541 & 3641 & 3178 & 3219 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of partitioning results: Metis, KL, genetic, and proposed algorithm. Figure 7: Ratio of proposed algorithm to other algorithms. The graph compares the ratio of the minimum values achieved by the proposed algorithm and other algorithms across the same test cases. A lower ratio indicates that the proposed algorithm performs better in optimizing the minimum cut edges compared to the other algorithms.