# L-rCBF: Learning-Based Key-Value Data Structure for Dynamic Data Processing
## 5 Performance Evaluation
### Performance Comparison of rCBF, L-FBF, and L-rCBF
Let \(n_{v}\) be the number of elements programmed into a verification structure (i.e., \(|S_{v}|=|S_{FR}\cup S_{FN}\cup B_{FP}|\)), \(m_{v}\) the number of cells in the verification structure, \(\alpha_{v}\) the size factor of the verification structure (i.e., \(\alpha_{v}=\frac{m_{v}}{n_{v}}\)), and \(\alpha_{b}\) the size factor of the FR-BF (i.e., \(\alpha_{b}=\frac{m_{b}}{n_{b}}\)). The L-rCBF\({}_{1}\) comprises Model\({}_{1}\), a 32\(n_{b}\)-bit FR-BF, and an 8\(n_{v}\)-cell V-rCBF (i.e., \(\alpha_{b}=32\) and \(\alpha_{v}=8\) in the L-rCBF\({}_{1}\)). To allocate the same amount of memory as in the L-rCBF\({}_{1}\), the size factors of the FR-BFs and verification structures should be adjusted in the L-FBF\({}_{1}\), L-FBF\({}_{2}\), and L-rCBF\({}_{2}\). For the FR-BF, \(\alpha_{b}\) depends on the model accuracy. As the accuracy of the model increases, \(n_{tp}\) increases and \(n_{b}\) decreases. To satisfy the condition \(n_{fp,b}<1\) until 15% of the elements are deleted in the learning-based structures, each \(\alpha_{b}\) in the L-rCBF\({}_{2}\) and L-FBF \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Model\({}_{1}\)** & **Model\({}_{2}\)** \\ \hline Number of weights (\(w\)) & 6207 & 48,055 \\ Memory requirements (kB) & 24.828 & 192.22 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of memory requirements of two models. Figure 3: Number of false positives from the FR-BF in the L-rCBF\({}_{1}\) with Model\({}_{1}\) according to the elements deleted. using Model\({}_{2}\) with a higher accuracy than Model\({}_{1}\) should be increased to increase \(m_{b}\), considering (11). In other words, \(\alpha_{b}\) in the L-FBF\({}_{1}\) is the same as that in the L-rCBF\({}_{1}\) (i.e., 32) because both structures use Model\({}_{1}\). However, each \(\alpha_{b}\) in the L-FBF\({}_{2}\) and L-rCBF\({}_{2}\) is set to 49 to satisfy the condition. Hence, to support deletions, \(\alpha_{b}\) should be increased as the accuracy of the model increases. A verification structure is constructed with the remaining memory after constructing a model and FR-BF from the total memory. We assume that \(R=2\) and \(L=3\) because six values exist. A single cell in an rCBF has five bits (i.e., \(R+L\) bits), whereas a single cell in an FBF has three bits (i.e., \(L\) bits). Therefore, if an L-FBF and L-rCBF include the same model, the \(\alpha_{v}\) of the V-FBF in the L-FBF is greater than that of the V-rCBF in the L-rCBF. Therefore, the \(\alpha_{v}\) in the L-FBF\({}_{1}\) is 13.33, 14.03 in the L-FBF\({}_{2}\), and 8.42 in the L-rCBF\({}_{2}\). In addition, the size factor of the single rCBF is 6.19. Table 2 compares the _undeletable_ rates of the rCBF, L-FBF\({}_{1}\), L-FBF\({}_{2}\), L-rCBF\({}_{1}\), and L-rCBF\({}_{2}\) when using the same amount of memory. No UNDEL-FPs from the rCBF and L-FBFs are observed because the structures return more UNDEL-Cs than the L-rCBFs. However, the total number of undeletables from each L-rCBF is less than those from the rCBF and L-FBFs. In terms of the deletion performance, structures using rCBFs outperform those using FBFs because of their counter fields. Even though each V-FBF in the L-FBFs has more cells than each V-rCBF in the L-rCBFs, the undeletable rates of the L-rCBF\({}_{1}\) and L-rCBF\({}_{2}\) improve by 83.67% and 76.67% compared with those of the L-FBF\({}_{1}\) and L-FBF\({}_{2}\), respectively. Table 3 compares the _search failure_ rates of the rCBF, L-FBF\({}_{1}\), L-FBF\({}_{2}\), L-rCBF\({}_{1}\), and L-rCBF\({}_{2}\) when using the same amount of memory. The reduction rate in search failures represents the proportion of reduced search failures observed in a learning-based structure relative to the single rCBF. The four learning-based structures improve the search failure rates compared with the single rCBF. When comparing L-FBFs with L-rCBFs, the search failure rates of the L-FBFs are better than those of the L-rCBFs because the \(\alpha_{v}\) of the V-FBFs (i.e., 13.33 and 14.03) are greater than those of the V-rCBFs (i.e., 8 and 8.42).