# L-rCBF: Learning-Based Key-Value Data Structure for Dynamic Data Processing
## 6 Conclusions  
In this paper, we propose an L-rCBF for dynamic data and design a deletion algorithm for the L-rCBF that can be applied to deletions in an L-FBF. The proposed L-rCBF can be utilized in various applications involving repetitive update operations (i.e., insertions and deletions), such as PIT lookup in NDN and deduplication in distributed systems. As an expandable and deletable key-value structure, the L-rCBF allows efficient operations and can achieve the purpose of each application without other data structures.  
Using the same amount of memory, the proposed L-rCBF is better than a single rCBF in terms of _undeletables_ and _search failures_ because a model in the L-rCBF consumes a relatively small amount of memory, regardless of the amount of data. Hence, as the amount of positive data to be stored increases, the L-rCBF becomes more efficient than a single rCBF.  
Using the same amount of memory, an L-rCBF is better than an L-FBF with the same model in terms of _undeletables_ because an rCBF can utilize cells with hash collisions for deletion, unlike an FBF. Moreover, as the number of return values increases, the L-rCBF becomes more efficient than the L-FBF. Therefore, for dynamic data processing with frequent insertions and deletions, the proposed L-rCBF is more suitable than the L-FBF, and deletions from the L-rCBF and L-FBF can be implemented using the proposed deletion algorithm. In addition, the theoretical analyses and experiments demonstrated the superiority of structures using an rCBF.  
Furthermore, the performance of a learning-based structure can vary depending on the accuracy of the model used. In other words, the higher the accuracy of a model, the better the deletion and search performance of the learning-based structure. Despite the higher memory requirement of a model with high accuracy compared with a model with lower accuracy, the accurate model reduces the sizes of the auxiliary structures (i.e., the FR-BF and verification structure) by reducing the number of elements stored in the structures, thereby enhancing the overall performance. However, owing to the tradeoff between memory requirements and accuracy, the size of a learned model cannot be increased in an unlimited manner to improve accuracy when designing a learning-based structure. In addition, if a complex model is designed to increase accuracy, the training time of the model increases as well as the memory requirement. Therefore, if reconstructions occur, the processing speed of the L-rCBF using the complex model is degraded compared to the L-rCBF using a simpler and smaller model.  
Conceptualization, H.B.; methodology, H.B.; software, Y.L.; validation, Y.L.; and H.B.; formal analysis, H.B.; investigation, Y.L. and H.B.; resources, H.B.; data curation, Y.L.; writing--original draft preparation, Y.L.; writing--review and editing, H.B.; visualization, Y.L.; supervision, H.B.; project administration, H.B.; funding acquisition, H.B. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (NRF-2021R1F1A1051646).  
Not applicable.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} BF & Bloom filter \\ FBF & Functional Bloom filter \\ rCBF & Counting Bloom filter with return values \\ \end{tabular}