# Time-Universal Data Compression +
## 3 The Time-Universal Code for the Finite Set of Data Compressors
### Experiments  
We conducted several experiments to evaluate the effectiveness of the proposed approach in practice. For this purpose we took 20 data compressor from the \"squeeze chart (lossless data compression benchmarks)\", [[http://www.squeezeechart.com/index.html](http://www.squeezeechart.com/index.html)]([http://www.squeezeechart.com/index.html](http://www.squeezeechart.com/index.html)) and files from this site [http://corpus.canterbury.ac.nz/descriptions/](http://corpus.canterbury.ac.nz/descriptions/), and [[http://tolstoy.ru/creativity/90-volume-collection-of-the-works/](http://tolstoy.ru/creativity/90-volume-collection-of-the-works/)]([http://tolstoy.ru/creativity/90-volume-collection-of-the-works/](http://tolstoy.ru/creativity/90-volume-collection-of-the-works/)) (Information about their size is given in the tables below). It is worth noting, that we do not change the collection of the data compressors and the files during experiments. The results are presented in the following tables, where the expression \"worst/best\" means the ratio of the longest length of the compressed file and the shortest one (for different data compressors). More formally, \(worst/best=\max_{i,j=1,\ldots,20}\left(|\varphi_{i}|/|\varphi_{j}|\right)\). The expression \"chosen/best\" is a similar value for a chosen data compressor and the best one. The value \"chosen/best\" is the frequency of occurrence of the event \"the best compressor was selected\". Table 3 shows the results of the two-step method, where we took 3% in the first step. Thus, the total extra time is limited to 20 \(\times\) 0.03 = 0.6, i.e., \(\delta\leq\) 0.6. Here ratio \"chosen best\" means a proportion of cases in which the best method was chosen. Table 4 shows the effect of the extra time \(\delta\) on the efficiency of the method (In this case we took 5% in the first step). Table 5 contains information about the three step method. Here we took 3% in the first step and then took five data compressors with the best performance. Then, in the second step, we tested those five data compressors taking 5% from the file. Hence, the extra time equals \(20\times 0.03+5\times 0.05=0.85\). Table 6 gives an example of four step method. Here we took 1% in the first step and then took five data compressors with the best performance. Then, in the second step, we tested those five data compressors taking 2% from each file. Basing on the obtained data, we chose three best and tested them on 5% parts. At last, the best of them was used for compression of the whole file. Hence, the extra time equals \(20\times 0.01+5\times 0.02+3\times 0.05=0.45\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Length of File (byte)** & **Number of Files** & **Ratio “Chosen Best”** & **Average “Worst/Best”** & **Average “Chosen/Best”** \\ \hline \(\leq 10^{5}\) & 1496 & 16\% & 112.87\% & 102.14\% \\ \(10^{5}\)-\(10^{6}\) & 1122 & 53.63\% & 131.22\% & 101.33\% \\ \(10^{6}\)–\(10^{8}\) & 384 & 73\% & 147.95\% & 100.84\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Two-step compression. Extra-time \(\delta\) = 20 \(\times\) 0.05 = 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Length of File (byte)** & **Number of Files** & **Ratio “Chosen Best”** & **Average “Worst/best”** & **Average “Chosen/Best”** \\ \hline \(\leq 10^{5}\) & 1496 & 8\% & 112.87\% & 103.57\% \\ \(10^{5}\)–\(10^{6}\) & 1122 & 45.72\% & 131.22\% & 102.04\% \\ \(10^{6}\)–\(10^{8}\) & 384 & 71\% & 147.95\% & 100.99\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Two-step compression. Extra-time \(\delta\) = 20 \(\times\) 0.03 = 0.6. If we compare Table 6 and Table 3, we can see that the performance of the four step method is better than two step method, where the extra time is significantly less for the four step method. The same is valid for the considered example of the three step method. We can see that the three- and four-step methods make sense because they make it possible to reduce the additional time while maintaining the better quality of the method.