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Conception et Analyse de quelques Algorithmes Distribués Probabilistes

Abstract : distributed system is an environment where multiple processes can work together to achieve a common goal. Processes can only directly communicate with their neighbours. Distributed algorithms aims to describe the tasks that can be executed in such systems. In other words, it seeks to determine what are the global behaviors that can be obtained in such systems, where processes behaviors have local effects. Network elements are called "nodes" and they are distinguished from each other by identifiers (such as an IP address on the Internet), but more generally, it is the position of each node in the network that distinguishes it. What characterizes distributed systems is that there is no centralized system that can comprehensively coordinate the different processes. The work of this thesis fit into this context and presents the evolution and performance of the algorithms analysis. These probabilistic algorithms are fully distributed and decentralized, executed in distributed systems that are anonymous, asynchronous and with different topologies. Firstly, we propose and study a uniform probabilistic election algorithm applied on graphs with triangular grids. This algorithm is based on using random delays associated with deletable nodes (simplicial nodes). These delays are independent and can be generated locally by vertices as they become deletable. For the class of graphs cited above, our main result is the introduction of an election algorithm that is totally fair, i.e. regardless of the vertex location in the graph, it will have the same probability of being elected as the other vertices. Secondly, we introduce and analyze two probabilistic distributed algorithms for a minimum spanning tree construction. These algorithms are essentially based on the Handshake algorithm. First, each edges on which a meeting took place (or isolated vertex) is considered a sub-spanning tree. Each execution of the algorithm, all sub-spanning trees are merged. The execution continues until all sub-spanning trees are merged into one. Thereafter, we prove that the constructed graph is a minimum spanning tree. Finally, we present a simulation platform for distributed algorithms which allows us to implement, test, and verify distributed algorithms programmed in the form of local computations, especially those described in the rewrite rules.
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Submitted on : Monday, October 28, 2019 - 7:20:34 PM
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El Mehdi Stouti. Conception et Analyse de quelques Algorithmes Distribués Probabilistes. Complexité [cs.CC]. Université Abdelmalek Essaâdi, 2016. Français. ⟨tel-02336469⟩

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