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This paper describes a fast and efficient method for minimization of two level single output Boolean functions.The minimization problem is reduced to that of coloring of the graph of incompatibility of implicanm.The program permits also to remove static hazards and allows inversion of output's polarity which proves to be very convenient when designing with PAL's, It gives solutions within a very reasonable amount of time.On small industrial examples its speed is slightly better than Espresso and it occupies 6 times less memory.

Mining frequent subgraphs is an interesting and important problem in the graph mining field, in that mining frequent subgraphs from a single large graph has been strongly developed, and has recently attracted many researchers. Among them, MNI-based approaches are considered as state-of-the-art, such as the GraMi algorithm. Besides frequent subgraph mining (FSM), frequent closed frequent subgraph mining was also developed. This has many practical applications and is a fundamental premise for many studies. This paper proposes the CloGraMi (Closed Frequent Subgraph Mining) algorithm based on GraMi to find all closed frequent subgraphs in a single large graph. Two effective strategies are also developed, the first one is a new level order traversal strategy to quickly determine closed subgraphs in the searching process, and the second is setting a condition for early pruning a large portion of non-closed candidates, both of them aim to reduce the running time as well as the memory requirements, improve the performance of the proposed algorithm. Our experiments are performed on five real datasets (both directed and undirected graphs) and the results show that the running time as well as the memory requirements of our algorithm are significantly better than those of the GraMi-based algorithm.INDEX TERMS data mining; frequent closed subgraph; social network; pruning strategy.

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.

Large graphs are often used to simulate and model complex systems in various research and application fields. Because of its importance, frequent subgraph mining (FSM) in single large graphs is a vital issue, and recently, it has attracted numerous researchers, and played an important role in various tasks for both research and application purposes. FSM is aimed at finding all subgraphs whose number of appearances in a large graph is greater than or equal to a given frequency threshold. In most recent applications, the underlying graphs are very large, such as social networks, and therefore algorithms for FSM from a single large graph have been rapidly developed, but all of them have NP-hard (nondeterministic polynomial time) complexity with huge search spaces, and therefore still need a lot of time and memory to restore and process. In this article, we present an overview of problems of FSM, important phases in FSM, main groups of FSM, as well as surveying many modern applied algorithms. This includes many practical applications and is a fundamental premise for many studies in the future.

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