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