## 3 Comprehensive Analysis of Issues of CIM-Based DMS Using RDB
### Degradation of Topology Processing Performance
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Binary Tree** & **B\(-\)Tree** & **B+Tree** \\ \hline Number of child nodes & Up to 2 child nodes & \begin{tabular}{c} Multiple child nodes \\ (the number can be defined) \\ \end{tabular} & \begin{tabular}{c} Multiple child nodes \\ (the number can be defined) \\ \end{tabular} & \begin{tabular}{c} Multiple child nodes \\ (the number can be defined) \\ \end{tabular} \\ \hline Data storage location & Key and value are stored at the node & Key and value are stored at both the internal and leaf nodes & \begin{tabular}{c} Only the key is stored at the internal node, and the actual \\ data are stored at the leaf node \\ \end{tabular} \\ \hline Index structure & Data are searched based on the key & \begin{tabular}{c} Multiple child nodes \\ (the number can be defined) \\ \end{tabular} & \begin{tabular}{c} Multiple child nodes \\ (the number can be defined) \\ \end{tabular} \\ \hline \multirow{4}{*}{Data storage location} & Key and value are stored at the node & Key and value are stored at both the internal and leaf nodes & \begin{tabular}{c} Only the key is stored at the internal node, and the actual \\ data are stored at the leaf node \\ \end{tabular} \\ \hline Index & Data are searched based on the key & \begin{tabular}{c} This index structure is \\ mainly used in large DBs or \\ file systems \\ \end{tabular} & \
\begin{tabular}{c} This structure is widely \\ used in a large DB system. \\ \end{tabular} \\ \cline{1-1}  & Data search, insert, and & search are supported by &
\begin{tabular}{c} Single for range search \\ and sequential access \\ \end{tabular} \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of Binary Tree, B\(-\)Tree, and B+Tree. exploration in RDB. This issue becomes particularly pronounced in databases handling large-scale systems. To extract and analyze topology information effectively, a faster search speed is advantageous. Equation (1) reflects the worst-case time complexity of an RDB, which requires multiple nested joins to process relational queries. \[O(h_{RDB})=O\Big{(}n^{2}\Big{)} \tag{1}\]  
Figure 9 depicts an example of topology processing using data stored in an RDB based on the conceptual model presented in Figure 2. When exploring Terminal8 for the first time, it is essential to verify that the IDs of the ConnectivityNode and ConductingEquipment connected to Terminal8 are 7 and 9, respectively. Subsequently, the next step involves searching for the Terminal with ConnectivityNode ID 7'. As the only primary key, ID, of the Terminal table permits index searching, it becomes necessary to search through all Terminals to confirm if the ConnectivityNode ID is 7'. Therefore, the time complexity of the RDB search increases to \(O\big{(}n^{2}\big{)}\). Conversely, in a B+Tree structure, employing index search yields a time complexity of \(O(n\log_{2}n)\). However, since the ConductingEquipment and ConnectivityNode fields lack primary key status, index search remains unattainable. Figure 8: RDB schema design for topology processing. Figure 9: An example of topology processing using data in an RDB.