# Spectrum Allocation Using Integer Linear Programming and Kerr Optical Frequency Combs
## 3 Results and Discussion
While the execution times for the proposed method are longer, this is attributable to the exploration of multiple dimensions, including client requirements, modulation formats, and available OFC  
Figure 6: Number of rejections vs. bandwidth and number of requests for the method propose in [19]. The highest BBR values are highlighted with red ellipses, indicating critical points in the analysis. Additionally, a dotted red line marks the point where the allocation method begins to show a decline. Figure 7: Number of rejections vs. bandwidth and number of requests using the FF method. The highest BBR values are highlighted with red ellipses, indicating critical points in the analysis. Additionally, a dotted red line marks the point where the allocation method begins to show a decline. channels, resulting in a more complex three-dimensional problem. It is worth noting that heuristic methods like FF, RWA, and RMLSA-OFC achieve faster performance; however, our approach excels at effectively managing a significantly larger number of client requests. For instance, with 1000 requests, the FF method processes in 9.24 s, whereas the proposed method requires approximately 122.86 min. This additional computational effort, however, results in superior network optimization, enabling more efficient resource allocation and significantly reducing blocking probability, thereby enhancing Quality of Service (QoS). To mitigate the longer execution times, future work could explore hardware acceleration techniques such as GPUs or FPGAs, which can substantially improve processing speeds given the three-dimensional array structure of the algorithm. Additionally, these tests were conducted on a system with 8 GB of RAM and a four-core 64-bit CPU with SSE2 support, which inevitably impacts execution times. Upgrading the hardware infrastructure could further enhance performance without compromising the achieved improvements. Although the proposed method is computationally intensive, its ability to effectively manage a higher number of clients per request makes the effort worthwhile, as it leads to significant improvements in service quality. Figure 8: Number of rejections vs. bandwidth and number of requests RWA method. The highest BBR values are highlighted with red ellipses, indicating critical points in the analysis. Additionally, a dotted red line marks the point where the allocation method begins to show a decline. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Request** & **Method FF** & **Method RWA** & **RMLSA-OFC** &
\begin{tabular}{c} **Proposed** \\ **Method** \\ \end{tabular} \\ \cline{2-5}
**Number** & **t (s)** & **t (s)** & **t (s)** & **t (s)** \\ \hline
1 & 1.042 s & 1.054 s & 1.06 s & 12.123 s \\ \hline
5 & 1.101 s & 1.215 s & 1.281 s & 42.236 s \\ \hline
10 & 1.153 s & 1.187 s & 1.333 s & 80.743 s \\ \hline
50 & 1.823 s & 1.985 s & 2.005 s & 314.806 s \\ \hline
100 & 2.131 s & 2.412 s & 2.311 s & 651.475 s \\ \hline
500 & 6.073 s & 6.150 s & 6.254 s & 3589.276 s \\ \hline
1000 & 9.241 s & 9.298 s & 9.420 s & 7371.629 s \\ \hline
1400 & 12.024 s & 12.098 s & 12.208 s & 6621.625 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative computation times.