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Optimization problems with propagation in graphs : Parameterized complexity and approximation

Abstract : In this thesis, we investigate the computational complexity of optimization problems involving a “diffusion process” in a graph. More specifically, we are first interested to the target set selection problem. This problem consists of finding the smallest set of initially “activated” vertices of a graph such that all the other vertices become activated after a finite number of propagation steps. If we modify this process by allowing the possibility of protecting'' a vertex at each step, we end up with the firefighter problem that asks for minimizing the total number of activated vertices by protecting some particular vertices. In fact, we introduce and study a generalized version of this problem where more than one vertex can be protected at each step. We propose several complexity results for these problems from an approximation point of view and a parameterized complexity perspective according to standard parameterizations as well as parameters related to the graph structure.
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Morgan Chopin. Optimization problems with propagation in graphs : Parameterized complexity and approximation. Other [cs.OH]. Université Paris Dauphine - Paris IX, 2013. English. ⟨NNT : 2013PA090023⟩. ⟨tel-00933769⟩

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