## 2 Literature Review  
This section provides a comprehensive overview of the methods proposed by the researchers for the topmost frequent regular pattern mining algorithms. However, these methods suffer from several issues. Firstly, these methods are computationally intensive because they follow the classical Apriori approach for the required pattern mining. Secondly, the methods are inadequate because they are applicable on static datasets and have no synopsis structure available to find patterns from online datasets. Thirdly, the K semantics of a parameter where all the topmost regular frequent patterns does not consider the distinct K support count as topmost-K frequent patterns; rather, if the topmost-K patterns with the same support are found, it stops mining further distinct K topmost-K support patterns. Fourthly, none of these methods apply pruning methods, other than the least support threshold from the top-K list. A detailed review of the topmost-K regular frequent pattern mining research can be found in [15]. However, a top-level comparison of the available relevant methods, along with the proposed method, is presented in Table 1 and discussed in the following paragraphs. [PERSON] et al. [2] have proposed top-K regular frequent patterns from transactional datasets, namely MTKPP. This approach performs a single scan of a given dataset to record the TIDs in which the corresponding items appear. The MTKPP uses a top-K list for ranking and recording top-K frequent regular patterns. The procedure discovers the patterns by performing breadth-first traversal of the search space. The support of every pattern is determined by TIDs' intersection mechanism. The patterns with their support and regularity are checked against the minimum support of the patterns in the top-K List and the user-given regularity threshold. A discovered pattern is merged with the patterns in the top-K list if the pattern's support is greater than the minimum support and its regularity is less than or equal to a user's given regularity threshold. However, the main issues with MTKPP are the excessive candidate generations and heavy memory consumptions due to \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**S. No**} & \multirow{2}{*}{**Method Name**} & **Support** & **Dataset** & **Summary Data** \\  & & **Threshold/Top-K** & **(Online/Offline)** & **Structure** \\ \hline
1 & MTKKP [2] & Top-K & Offline & No \\
2 & TR-CT [12] & Top-K & Offline & No \\
3 & TKIRMPE [19] & Top-K & Offline & No \\
4 & TFRC-Mine [21] & Top-K & Offline & No \\
5 & PF-ECLAT [22] & Support threshold & Offline & No \\
6 & IMTFRI [20] & Top-K & Online & Yes \\
7 & TKFM [15] & Top-K & Offline & No \\
8 & TKIFIs Miner [14] & Top-K & Offline & No \\
8 & TKIFRPM (Proposed) & Top-K & Online & Yes \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Top-level comparison of the topmost frequent regular pattern mining methods. the in-memory placement of the TIDs of all the items without compression, which could compromise the performance of MTKPP on sparse and dense datasets. [PERSON] et al. [12] have proposed an approach in another research work on the top-K frequent regular pattern mining, namely TR-CT (top-K regular frequent itemset mining based on compressed TIDs). The TR-CT approach uses a top-K list and works using a best-fit strategy, similar to MTKPP. The TR-CT merges the itemsets (based on common prefixes) to present in the top-K list and finds their support by intersecting their compressed TIDs. The discovered itemsets, along with their support and regularity, are ranked in the top-K list. The performance of TR-CT on sparse datasets is similar to that of MTKPP. However, TR-CT is found to be more efficient than the MTKPP technique on dense datasets by requiring less memory due to the compression of the consecutive TIDs. In another work, [PERSON] et al. [19] have proposed another approach, namely TKRIMPE (top-K regular-frequent itemset mining with dataset partitioning and support estimation), which is more efficient than TR-CT on sparse datasets.