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Detecting Existence of Cycles in Petri Nets

An Algorithm that Computes Non-redundant (Nonzero) Parts of Sparse Adjacency Matrix

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International Joint Conference SOCO’16-CISIS’16-ICEUTE’16 (SOCO 2016, CISIS 2016, ICEUTE 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 527))

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Abstract

Literature study reveals the existence of many algorithms for detecting cycles (also known as circuits) in directed graphs. Majority of these algorithms can be classified into two groups: (1) traversal algorithms (e.g. variants of depth-first-search algorithms), and (2) matrix-based algorithms (manipulation of the adjacency matrix and its power series). Adjacency matrix based algorithms are computationally simple and more compact than the traversal algorithms. However, a Petri net, due to its bipartite nature, possesses sparse matrix as adjacency matrix. Hence, the matrix based algorithms become inefficient as the algorithm work through redundant data most of its running time. In this paper, we take a closer look into the structure of the adjacency matrix of a Petri net and then propose an algorithm for detecting existence of cycles; the proposed algorithm is computationally efficient as its works through non-redundant data only, as well as simple, easy to understand and easy to implement.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Stavanger, Stavanger, Norway

    Reggie Davidrajuh

Authors
  1. Reggie Davidrajuh
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Correspondence to Reggie Davidrajuh .

Editor information

Editors and Affiliations

  1. Computational Intelligence Group, University of the Basque Country (UPV/EHU), San Sebastian, Spain

    Manuel Graña

  2. University of the Basque Country, Vitoria, Spain

    José Manuel López-Guede

  3. Computational Intelligence Group, University of the Basque Country (UPV/EHU), San Sebastian, Spain

    Oier Etxaniz

  4. Department of Civil Engineering, University of Burgos, Burgos, Spain

    Álvaro Herrero

  5. University of Salamanca, Salamanca, Spain

    Héctor Quintián

  6. University of Salamanca, Salamanca, Spain

    Emilio Corchado

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Davidrajuh, R. (2017). Detecting Existence of Cycles in Petri Nets. In: Graña, M., López-Guede, J.M., Etxaniz, O., Herrero, Á., Quintián, H., Corchado, E. (eds) International Joint Conference SOCO’16-CISIS’16-ICEUTE’16. SOCO CISIS ICEUTE 2016 2016 2016. Advances in Intelligent Systems and Computing, vol 527. Springer, Cham. https://doi.org/10.1007/978-3-319-47364-2_36

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  • DOI: https://doi.org/10.1007/978-3-319-47364-2_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-47363-5

  • Online ISBN: 978-3-319-47364-2

  • eBook Packages: EngineeringEngineering (R0)

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