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A Formal Approach for Maintaining Forest Topologies in Dynamic Networks

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Book cover Computer and Information Science (ICIS 2017)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 719))

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Abstract

In this paper, we focus on maintaining a forest of spanning trees in dynamic networks. In fact, we propose an approach based on two levels for specifying and proving distributed algorithms in a forest. The first level allows us to control the dynamic structure of the network by triggering a maintenance operation when the forest is altered. To do so, we develop a formal pattern using the Event-B method, based on the refinement technique. The proposed pattern relies on the dynamicity aware-graph relabeling systems (DA-GRS) which is an existing model for building and maintaining a spanning forest in dynamic networks. It is based on evolving graphs as a powerful model to record the evolution of a network topology. The second level of our approach deals with distributed algorithms which can be applied to spanning trees of the forest. Through an example of a leader election algorithm, we illustrate our pattern. The proof statistics show that our solution can save efforts on specifying as well as proving the correctness of distributed algorithms in a forest topology.

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Notes

  1. 1.

    \({\mathbb {N}1'}\) denotes the set of positive natural numbers: \({\mathbb {N}1=\mathbb {N}\backslash \{0\}}\).

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Author information

Authors and Affiliations

  1. ReDCAD Laboratory, FSEGS, University of Sfax, B.P. 1088, 3018, Sfax, Tunisia

    Faten Fakhfakh, Mohamed Tounsi & Ahmed Hadj Kacem

  2. LaBRI, Bordeaux INP, University of Bordeaux, CNRS UMR 5800, 33405, Talence, France

    Mohamed Mosbah

  3. LORIA Laboratory, University of Lorraine, CNRS UMR 7503, Nancy, France

    Dominique Méry

Authors
  1. Faten Fakhfakh
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  2. Mohamed Tounsi
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  3. Mohamed Mosbah
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  4. Dominique Méry
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  5. Ahmed Hadj Kacem
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Corresponding author

Correspondence to Faten Fakhfakh .

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Editors and Affiliations

  1. Software Engineering and Information Technology Institute, Central Michigan University, Mt. Pleasant, MI, USA

    Roger Lee

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Fakhfakh, F., Tounsi, M., Mosbah, M., Méry, D., Kacem, A.H. (2018). A Formal Approach for Maintaining Forest Topologies in Dynamic Networks . In: Lee, R. (eds) Computer and Information Science. ICIS 2017. Studies in Computational Intelligence, vol 719. Springer, Cham. https://doi.org/10.1007/978-3-319-60170-0_9

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  • DOI: https://doi.org/10.1007/978-3-319-60170-0_9

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