CCGraMi: An Effective Method for Mining Frequent Subgraphs in a Single Large Graph

Abstract

In modern applications, large graphs are usually applied in the simulation and analysis of large complex systems such as social networks, computer networks, maps, traffic networks. Therefore, graph mining is also an interesting subject attracting many researchers. Among them, frequent subgraph mining in a single large graph is one of the most important branches of graph mining, it is defined as finding all subgraphs whose occurrences in a dataset are greater than or equal to a given frequency threshold. In which, the GraMi algorithm is considered the state of the art approach and many algorithms have been proposed to improve this algorithm. In 2020, the SoGraMi algorithm was proposed to optimize the GraMi algorithm and presented an outstanding performance in terms of runtime and storage space. In this paper, we propose a new algorithm to improve SoGraMi based on connected components, called CCGraMi (Connected Components GraMi). Our experiments on four real datasets (both directed and undirected) show that the proposed algorithm outperforms SoGraMi in terms of running time as well as memory requirements.

Subgraph mining in a large graph: A review

“…Based on these two phases, algorithms focus on reducing redundant candidates or methods (N.‐T. Le et al, 2020; Nguyen et al, 2020) to reduce costs for the testing phase (Nguyen, Zelinka, & Diep, 2021).…”

“…Solving the isomorphism problem (Nabti, 2017) is NP‐complete, and the runtime of mining algorithms should be exponential (Elseidy et al, 2014; Yan & Han, 2002). Therefore, there are many algorithms that have been proposed to reduce the running time for determining isomorphisms, such as GraMi (Elseidy et al, 2014), SoGraMi (Nguyen et al, 2020), and CCGraMi (Nguyen, Zelinka, et al, 2021). For the small subgraph S in Figure 1 determining the isomorphism is quite easy, but for larger subgraphs like S 1 in Figure 5, determining all isomorphisms becomes very complicated, as in Table 2.…”

“…The BaGraMi algorithm searches all isomorphisms to early prune all invalid assignments in the domain of all candidates. In 2021, the CCGraMi algorithm (Nguyen, Zelinka, & Diep, 2021) proposed two effective strategies to test candidate subgraphs based on connected components: searching isomorphisms and pruning subgraphs' domains. This algorithm has good results in comparison to original GraMi algorithm (Elseidy et al, 2014) and optimized SoGraMi algorithm (Nguyen et al, 2020) in terms of running time and memory requirements.…”

“…Typically, FSM algorithms (Jiang et al, 2013) need two main phases, generating and testing (Elseidy et al, 2014;Yan & Han, 2002) and using methods to search and count the isomorphisms of candidates in a large graph. Based on these two phases, algorithms focus on reducing redundant candidates or methods (N.-T. Le et al, 2020;Nguyen et al, 2020) to reduce costs for the testing phase (Nguyen, Zelinka, & Diep, 2021).…”