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Granular computing (GrC) is a methodology for reducing the complexity of problem solving and includes two basic aspects: granulation and granular-based computing. Strongly connected components (SCCs) are a significant subgraph structure in digraphs. In this paper, two new granulation strategies were devised to improve the efficiency of computing SCCs. Firstly, four SCC correlations between the vertices were found, which can be divided into two classes. Secondly, two granulation strategies were designed based on correlations between two classes of SCCs. Thirdly, according to the characteristics of the granulation results, the parallelization of computing SCCs was realized. Finally, a parallel algorithm based on granulation strategy for computing SCCs of simple digraphs named GPSCC was proposed. Experimental results show that GPSCC performs with higher computational efficiency than algorithms. [ABSTRACT FROM AUTHOR]

Meta-heuristic algorithms have been extensively utilized in feature selection tasks because they can obtain the global optimal solution. However, the meta-heuristic algorithm will take too much time in the face of a large number of samples. Although most of the studies compromise to approximate optimal solutions for avoiding time-consuming problems, a new problem with reduced classification performance, especially classification stability, is then generated. Aiming to above problems, this paper proposes a new feature selection framework. First, this framework exploits a voting ensemble strategy to improve classification stability by reducing the impact of misclassified labels on the overall classification results. Second, the framework uses a data perturbation strategy to enhance classification accuracy. In particular, the data perturbation strategy is able to generate more neighborhood relationships in the dataset, which could reveal the distribution of various features of the samples. A voting ensemble of different feature distributions is capable of extracting more information from the dataset, then the initially misclassified samples are more likely to be returned to the correct classification. Third, the framework takes a random sampling accelerator into account to solve the problem of excessive time consumption by reducing the size of the search sample space. Finally, for the sake of verifying the effectiveness of the proposed framework, four meta-heuristic feature selection methods based on a neighborhood rough set are compared on 20 datasets. The experimental results indicate that our framework could improve classification performance and accelerate feature selection, particularly in confronting large sample sizes. [ABSTRACT FROM AUTHOR]

Symmetry is one of the most important aesthetic criteria on graph drawing. It is quite necessary to measure the extent to which the drawings can be considered symmetric. For this purpose, a symmetric metric based on vertex coordinate calculation is proposed in this paper. It is proven theoretically and experimentally that the proposed metric is robust to contraction, expansion, and rotation of drawings. This robustness conforms to human perception of symmetry. Star-subgraphs and cycles are two common structures in digraphs. Both of them have inherent symmetry which should be displayed in drawings. For this purpose, a force-directed algorithm named FDS is proposed which can draw star-subgraphs and cycles as symmetrically as possible. FDS algorithm draws cycles as circles whose positions are fixed to provide a scaffolding for overall layout, renders non-leaf vertices by a standard force-directed layout, and places leaf vertices on concentric circles via a deterministic strategy. A series of experiments are carried out to test FDS algorithm. The results show that FDS algorithm draws digraphs more symmetrically than the existing state-of-the-art algorithms and performs efficiency comparable to O(nlog⁡n) YFHu algorithm. [ABSTRACT FROM AUTHOR]