# A Method for Synthesizing Ultra-Large-Scale Clock Trees
## 2 IB-KSR Algorithm
### Balanced Split
Since the KSR algorithm is not suitable for ultra-large-scale clock tree synthesis, IB-KSR does not activate the IMST and Balanced Split modules in smaller-scale clock trees, and its performance is expected to closely resemble that of the native KSR algorithm. The comparison results are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Benchmark** & **Register** & **Algorithm** & **Global Skew (ps)** & **Average Clock Latency (ps)** & **Buffer Count** & **Overlap Area** & **Total Time (s)** \\ \hline Case1 & 121949 & IB-KSR & 145.0863 & 493.1913 & 3167 & 0.43\% & 252.33 \\  & & GSR & 231.6535 & 827.4057 & 2597 & 6.88\% & 2.93 \\ Case2 & 114261 & IB-KSR & 102.2597 & 518.1393 & 2970 & 0.31\% & 158.46 \\  & & GSR & 114.3043 & 526.4502 & 2651 & 3.99\% & 2.11 \\ Case3 & 139387 & IB-KSR & 112.2617 & 472.9788 & 3639 & 0.25\% & 251.36 \\  & & GSR & 158.3193 & 742.1908 & 3167 & 7.26\% & 3.02 \\ Case4 & 137783 & IB-KSR & 138.8413 & 631.1416 & 3549 & 0.29\% & 268.63 \\  & & GSR & 363.7603 & 887.4536 & 2906 & 6.14\% & 3.25 \\ Case5 & 184204 & IB-KSR & 152.9521 & 595.4133 & 4788 & 0.28\% & 331.92 \\  & & GSR & 319.6448 & 972.6395 & 4132 & 6.68\% & 3.59 \\ Case6 & 178852 & IB-KSR & 154.3807 & 519.8054 & 4657 & 0.33\% & 390.40 \\  & & GSR & 152.6932 & 797.166 & 3940 & 7.99\% & 4.01 \\ Case7 & 144441 & IB-KSR & 96.6709 & 552.9979 & 3822 & 0.39\% & 273.92 \\  & & GSR & 172.7921 & 473.3328 & 3296 & 8.61\% & 2.88 \\ Case8 & 138733 & IB-KSR & 148.5577 & 479.536 & 3698 & 0.18\% & 288.28 \\  & & GSR & 217.1041 & 799.3908 & 3039 & 6.62\% & 3.14 \\ Case9 & 166093 & IB-KSR & 117.9646 & 569.4214 & 4318 & 0.2\% & 354.01 \\  & & GSR & 434.5138 & 1211.0952 & 3519 & 7.29\% & 4.21 \\ Case10 & 184987 & IB-KSR & 211.6576 & 622.0583 & 4968 & 0.37\% & 314.48 \\  & & GSR & 259.0176 & 919.1639 & 4072 & 5.87\% & 3.98 \\ Average & & IB-KSR & 137.47 & 535.75 & 3953 & 0.3\% & 288.78 \\  & & GSR & 242.88 & 815.83 & 3257 & 6.83\% & 3.31 \\ Comparison & & \(\frac{\text{IE-KSR}}{\text{GSR}}\) & 0.57 & 0.66 & 1.21 & 0.04 & 87.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison between IB-KSR and GSR. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Benchmark** & **Register** & **Algorithm** & **Global Skew (ps)** & **Average Clock Latency (ps)** & **Total Time (s)** & **Average RSS (MB)** & **Max RSS (MB)** \\ \hline
10f01 & 1107 & IB-KSR & 55.5352 & 436.8898 & 0.096 & 5.049 & 8.520 \\  & & KSR & 54.5593 & 459.9714 & 0.220 & 20.813 & 35.212 \\
10f02 & 2249 & IB-KSR & 71.4987 & 616.7572 & 0.168 & 7.044 & 15.208 \\  & & KSR & 77.1856 & 677.0919 & 0.593 & 100.849 & 170.880 \\
10f03 & 1200 & IB-KSR & 18.8928 & 191.0488 & 0.057 & 7.012 & 10.540 \\  & & KSR & 27.7179 & 191.7802 & 0.151 & 30.035 & 51.144 \\
10f04 & 1845 & IB-KSR & 15.1817 & 216.4092 & 0.123 & 7.415 & 12.496 \\  & & KSR & 22.7395 & 203.2573 & 0.107 & 80.815 & 140.544 \\
10f05 & 1016 & IB-KSR & 16.7752 & 130.0987 & 0.077 & 6.311 & 10.564 \\  & & KSR & 11.5607 & 125.1863 & 0.129 & 13.567 & 38.14 \\  & & IB-KSR & 35.5767 & 330.4407 & 0.104 & 6.566 & 11.466 \\  & & KSR & 38.7526 & 331.3111 & 1.20 & 49.216 & 87.184 \\ Comparison & & \(\frac{\text{IE-KSR}}{\text{GSR}}\) & 0.92 & 0.997 & 0.087 & 0.13 & 0.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison between IB-KSR and KSR on ISPD 2010 benchmark tests. In small- to medium-scale clock tree synthesis, the performance metrics of IB-KSR are close to those of the native KSR algorithm. As the scale of the clock tree increases, the IMST and Balanced Split modules of IB-KSR begin to demonstrate their advantages. In smaller-scale scenarios, however, the performance of IB-KSR gradually converges to that of the KSR algorithm. This indicates that IB-KSR not only holds significant advantages in ultra-large-scale clock tree synthesis but also exhibits broad applicability across clock tree synthesis tasks of varying scales. Through a comparative analysis of Resident Set Size (RSS) metrics, IB-KSR demonstrates significantly superior memory efficiency that exhibits nonlinear scalability advantages.