# FSM-BC-BSP: Frequent Subgraph Mining Algorithm Based on BC-BSP
## 5 Conclusions and Future Work  
In recent years, the increased use of graph models to abstract scientific data has led to a surge in research on the mining of interesting patterns from large-scale graph data. Existing research primarily focuses on graph sets and single large graphs. However, the  
Figure 8: The times of frequent subgraphs with the same support under different datasets. Figure 9: The times of frequent subgraphs with the same support under different datasets. current algorithms for the mining of frequent subgraphs based on single large graphs face challenges such as high complexity and poor scalability. Moreover, they struggle to handle the mining of frequent subgraphs on a large single graph. Against this backdrop, this paper delves into the mining of frequent subgraphs on large graphs and introduces the FSM-BC-BSP algorithm to address the challenges associated with single-graph frequent subgraph mining. The algorithm utilizes the BC-BSP message-sending and message-receiving mechanism for data sharing across different stages of the frequent subgraph mining process. It employs standard subgraph coding, ensuring that identical subgraphs are sent to the same node for global support calculation on the large graph. Additionally, FSM-BC-BSP leverages the rightmost path expansion strategy to generate candidate subgraphs, minimizing redundancy. The use of standard coding helps to uniquely identify subgraphs, eliminating the need for subgraph isomorphism calculations. Furthermore, the algorithm adopts the MNI measurement method for support calculation, adhering to the downward closure attribute. Performance testing of the FSM-BC-BSP algorithm across various datasets, initial partition counts, and support levels yielded promising results. In comparison to the FSM-H and GRAMI algorithms, FSM-BC-BSP demonstrated superior performance. Particularly in scenarios with low support, FSM-BC-BSP showcased outstanding efficiency. The FSM-BC-BSP algorithm represents a valuable contribution to the field of frequent subgraph mining, offering an effective solution for large single-graph scenarios. The proposed algorithm's scalability, efficiency, and ability to handle low-support situations make it a noteworthy advancement in the realm of graph data mining. Certainly, this algorithm has inherent limitations--notably, the process of data transmission involves redundant static data that are required at each iteration step and remain unchanged. The algorithm proposed in this paper operates under the assumption that the input graph data are static. However, in practical applications, graph data often undergo frequent changes. For instance, within the DBLP user relationship graph, should a new author publish a paper, the graph structure would consequently experience some degree of alteration. This observation underscores the necessity for future research to focus on mining frequent subgraphs within dynamically changing graphs. Moreover, when it comes to accessing static data, the current algorithm can only sequentially match the static data stored on the hard disk. Indeed, as each frequent subgraph expands, the requisite static data are directly related to the current vertex data. Therefore, forthcoming research efforts should aim to establish a static data access model, designed to optimize the retrieval of such static data. Conceptualization, Y.B. ; Data curation, Y.B. ; Investigation, F.L. ([PERSON]); Methodology, F.L. (Fangling Leng); Software, F.L. ([PERSON]); Supervision, G.Y. ; Validation, T.Z. ; Visualization, F.L. (Fangling Leng); Writing--original draft, F.L. (Fangling Leng); Writing--review and editing, T.Z. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (grant numbers 62137001 and 62272093). Not applicable. Data Availability Statement: Data is contained within the article. The authors declare no conflicts of interest.