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Dynamic network formation

Abstract : This thesis focuses on the rapid mixing of graph-related Markov chains. The main contribution concerns graphs with local edge dynamics, in which the topology of a graph evolves as edges slide along one another. We propose a classification of existing models of dynamic graphs, and illustrate how evolving along a changing structure improves the convergence rate. This is complemented by a proof of the rapid mixing time for one such dynamic. As part of this proof, we introduce the partial expansion of a graph. This notion allows us to track the progression of the dynamic, from a state with poor expansion to good expansion at equilibrium. The end of the thesis proposes an improvement of the Propp and Wilson perfect sampling technique. We introduce oracle sampling, a method inspired by importance sampling that reduces the overall complexity of the Propp and Wilson algorithm. We provide a proof of correctness, and study the performance of this method when sampling independent sets from certain graphs.
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  • HAL Id : tel-02385281, version 1



Rémi Varloot. Dynamic network formation. Data Structures and Algorithms [cs.DS]. Université Paris sciences et lettres, 2018. English. ⟨NNT : 2018PSLEE048⟩. ⟨tel-02385281⟩



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