# Computing Maximal Lyndon Substrings of a String
## 7 Results  
This section contains the measurements of the average times for the datasets discussed in the previous section. For better understanding of the data, we present them in Tables 1-8 and Figures 7-14. All the graphs include the curve \(x=y\) for reference. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**String Length** & **Time in Ticks** & **Time in Ticks** & **Time in Ticks** \\  & **IDLA** & **TRLA** & **BSLA** \\ \hline
10 & \(3.699\times 10^{-1}\) & 1.579 & 1.080 \\
50 & 3.509 & \(1.037\times 10\) & 6.627 \\
100 & 8.898 & \(2.109\times 10\) & \(1.403\times 10\) \\
500 & \(6.403\times 10\) & \(1.123\times 10^{2}\) & \(7.228\times 10\) \\
1000 & \(1.431\times 10^{2}\) & \(2.332\times 10^{2}\) & \(1.544\times 10^{2}\) \\
5000 & \(8.749\times 10^{2}\) & \(1.207\times 10^{3}\) & \(9.039\times 10^{2}\) \\
10,000 & \(1.912\times 10^{3}\) & \(2.460\times 10^{3}\) & \(1.935\times 10^{3}\) \\
50,000 & \(1.134\times 10^{4}\) & \(1.280\times 10^{4}\) & \(1.110\times 10^{4}\) \\
100,000 & \(2.431\times 10^{4}\) & \(2.588\times 10^{4}\) & \(2.316\times 10^{4}\) \\
500,000 & \(1.383\times 10^{5}\) & \(1.390\times 10^{5}\) & \(1.781\times 10^{5}\) \\
1,000,000 & \(2.916\times 10^{5}\) & \(2.865\times 10^{5}\) & \(4.994\times 10^{5}\) \\
5,000,000 & \(1.643\times 10^{6}\) & \(1.968\times 10^{6}\) & \(3.752\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average times for dataset dna (\(10^{6}\)_clock ticks per second_). Figure 8: Average times for dataset dna (\(10^{6}\)_clock ticks per second_). Figure 10: Average times for dataset int (\(10^{6}\)_clock ticks per second_). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**String Length** & **Time in Ticks** & **Time in Ticks** & **Time in Ticks** \\  & **IDLA** & **TRLA** & **BSLA** \\ \hline
10 & \(3.547\times 10^{-1}\) & 1.645 & \(9.794\times 10^{-1}\) \\
50 & 3.032 & 9.992 & 5.609 \\
100 & 7.279 & \(2.032\times 10\) & \(1.153\times 10\) \\
500 & \(4.845\times 10\) & \(1.136\times 10^{2}\) & \(6.184\times 10\) \\
1000 & \(1.057\times 10^{2}\) & \(2.376\times 10^{2}\) & \(1.294\times 10^{2}\) \\
5000 & \(6.428\times 10^{2}\) & \(1.218\times 10^{3}\) & \(7.753\times 10^{2}\) \\
10,000 & \(1.388\times 10^{3}\) & \(2.544\times 10^{3}\) & \(1.796\times 10^{3}\) \\
50,000 & \(8.055\times 10^{3}\) & \(1.448\times 10^{4}\) & \(1.088\times 10^{4}\) \\
100,000 & \(1.710\times 10^{4}\) & \(2.943\times 10^{4}\) & \(2.379\times 10^{4}\) \\
500,000 & \(9.829\times 10^{4}\) & \(1.825\times 10^{5}\) & \(2.740\times 10^{5}\) \\ \(1,000,000\) & \(2.071\times 10^{5}\) & \(4.827\times 10^{5}\) & \(7.989\times 10^{5}\) \\ \(5,000,000\) & \(1.162\times 10^{6}\) & \(5.143\times 10^{6}\) & \(6.635\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average times for dataset int (\(10^{6}\)_clock ticks per second_). Figure 9: Average times for dataset eng (\(10^{6}\)_clock ticks per second_). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**String Length** & **Time in Ticks** & **Time in Ticks** & **Time in Ticks** \\  & **IDLA** & **TRLA** & **BSLA** \\ \hline
10 & \(4.588\times 10^{-1}\) & \(1.628\) & \(1.126\) \\
50 & \(4.987\) & \(1.039\times 10\) & \(7.112\) \\
100 & \(1.275\times 10\) & \(2.179\times 10\) & \(1.439\times 10\) \\
500 & \(9.033\times 10\) & \(1.101\times 10^{2}\) & \(6.914\times 10\) \\
1000 & \(2.060\times 10^{2}\) & \(2.222\times 10^{2}\) & \(1.392\times 10^{2}\) \\
5000 & \(1.319\times 10^{3}\) & \(1.171\times 10^{3}\) & \(7.699\times 10^{2}\) \\
10,000 & \(2.896\times 10^{3}\) & \(2.394\times 10^{3}\) & \(1.652\times 10^{3}\) \\
50,000 & \(2.209\times 10^{4}\) & \(1.263\times 10^{4}\) & \(8.992\times 10^{3}\) \\
100,000 & \(3.965\times 10^{4}\) & \(2.567\times 10^{4}\) & \(1.862\times 10^{4}\) \\
500,000 & \(2.233\times 10^{5}\) & \(1.349\times 10^{5}\) & \(1.091\times 10^{5}\) \\
1,000,000 & \(4.734\times 10^{5}\) & \(2.759\times 10^{5}\) & \(3.104\times 10^{5}\) \\
5,000,000 & \(2.632\times 10^{6}\) & \(1.458\times 10^{6}\) & \(2.298\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table}