Finding strongly connected components of simple digraphs based on granulation strategy

Xu, Taihua; Wang, Guoyin; Yang, Jie

doi:10.1016/j.ijar.2019.12.001

Cited by 14 publications

(6 citation statements)

References 37 publications

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“…Therefore, one of the main novelties of our approach is that each subsystem (or a subgroup of them as shown below) could be solved separately in a proper order based on the structure of the graph, making it possible for the following procedure that simplifies ISM simulation. Precisely, each output of a subsystem (or group of them: T. Xu et al [55]) becomes the input of the next subsystem in the chosen ordering. Matrix M can be structured as a block matrix to better describe what just said, each block representing a node (subsystem) and corresponding connections of the subsystem to another one, then represented as the sum of a strictly block lower triangular matrix M , and a strictly block upper triangular matrix M .…”

Section: The New Approach To Individual Subsystems Models: General As...mentioning

confidence: 99%

Interconnected Systems Modelling in Food Industry: General Solution Scheme and Stability Conditions for Linear Time-Invariant Systems

et al. 2023

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The problem of simulating complex systems, such as production lines, industrial plants, food processing, etc., today represents an opportunity that brings with it the great advantage of limiting design costs. However, nowadays the designer, after defining and implementing the mathematical models of the studied process, may need to rebuild the whole simulation framework because he needs to modify the model of even just one subsystem. It is for this reason that in this paper, a new framework for the use of Individual Subsystem Models (ISM) for the modelling and simulation of interconnected systems has been studied and implemented. Furthermore, the study of the state of the art has revealed the lack of efficient and sufficiently general numerical algorithms, but, at the same time, it is simple to use to solve the algebraic-differential equations deriving from the ISM simulation. The proposed new approach follows the paradigm of co-simulation methods, including graph theory methods, to solve the general ISM simply and efficiently. In this approach, each subsystem is required to have its own representation independently of the other subsystems. In this way, it is always possible to replace any subsystem whenever an updated representation becomes available, making maintenance and evolution of the entire ISM flexible. Our framework calls each subsystem separately in an optimal (suboptimal) order based on the structure of the graph. Each calculated output is transferred to the input of the next subsystem in the chosen. The general procedure has been validated in the context of Linear and Time-Invariant ISMs: in these hypotheses, the stability conditions have been calculated and numerical tests have been performed which show the effectiveness of the proposed approach.

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Section: The New Approach To Individual Subsystems Models: General As...mentioning

confidence: 99%

Interconnected Systems Modelling in Food Industry: General Solution Scheme and Stability Conditions for Linear Time-Invariant Systems

et al. 2023

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show abstract

“…Some serial [1][2][3][4][5][6][7][8] algorithms have been proposed for computing SCCs. Due to the inherent efficiency disadvantages of serial algorithms compared with parallel algorithms, some parallel [6,[9][10][11][12][13][14][15][16][17] algorithms have been proposed.…”

Section: Introductionmentioning

confidence: 99%

“…For SCCs problem solving, granulation strategies based on SCC correlations have been introduced. In [7], two nontrivial SCC correlations were found, and a granulation strategy was proposed based on them. Vertex granules corresponding to each vertex were constructed using the granulation strategy.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, the computational efficiency of SCCs was further enhanced. The time complexities of algorithms in [7,8] are both O(c•(n+m)), where c is the number of nontrivial SCCs.…”

Section: Introductionmentioning

confidence: 99%

“…Vertex granules were used to solve the problem of SCC discovery in a serial manner in [7,8]. However, they have inherent disadvantages in terms of efficiency.…”

Section: Introductionmentioning

confidence: 99%

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A Granulation Strategy-Based Algorithm for Computing Strongly Connected Components in Parallel

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Chen

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Mathematics

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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.

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An Acceleration Method for Attribute Reduction Based on Attribute Synthesis

Shi,

Xu,

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et al. 2023

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Finding strongly connected components of simple digraphs based on granulation strategy

Cited by 14 publications

References 37 publications

Interconnected Systems Modelling in Food Industry: General Solution Scheme and Stability Conditions for Linear Time-Invariant Systems

Interconnected Systems Modelling in Food Industry: General Solution Scheme and Stability Conditions for Linear Time-Invariant Systems

A Granulation Strategy-Based Algorithm for Computing Strongly Connected Components in Parallel

An Acceleration Method for Attribute Reduction Based on Attribute Synthesis

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