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Maintenance et simulation de graphes aléatoires dynamiques

Abstract : We study the problem of maintaining a given distribution of randomgraphs under an arbitrary sequence of vertex insertions and deletions. Keeping inmind our objective to model the evolution of dynamic logical networks, we work ina local model where we do not have direct access to the list of all vertices. Instead,we assume access to a global primitive that returns a random vertex, chosen uniformlyfrom the whole vertex set. The maintenance problem has been explored onseveral simple random graph models (Erdos–Rényi random graphs, pairing modelbased random graphs, uniform k-out graphs). For each model, one or several updatealgorithms for the maintenance task have been described and analyzed ; the mostelaborate of them are asymptically optimal. The maintenance task rise several simulationissues linked to our distributed context. In particular, we have focused onmaintenability of random graph distributions and simulability of families of probabilitydistributions over integers in our local random model. Special attention hasbeen paid to efficient simulation of particular distributions we were interested in(certain binomial distributions). The latter has been obtained through the use ofproperties of a new generation tree for permutations, which has been introducedalong the way
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Submitted on : Monday, December 7, 2015 - 9:46:06 AM
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  • HAL Id : tel-01238744, version 1

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Romaric Duvignau. Maintenance et simulation de graphes aléatoires dynamiques. Modélisation et simulation. Université de Bordeaux, 2015. Français. ⟨NNT : 2015BORD0177⟩. ⟨tel-01238744⟩

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