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Network partitioning algorithms with scale-free objective

Abstract : In light of the complexity induced by large-scale networks, the design of network partitioning algorithms and related problematics are at the heart of this thesis. First, we raise a preliminary question on the structure of the partition itself: as the parts may includes disconnected nodes, we want to quantify the drawbacks to impose the nodes inside each part to be connected. Then we study the design of a partitioning algorithm inducing a reduced scale-free network. This allows to take advantage of the inherent features of this type of network. We also focus on the properties to preserve to respect the physical and dynamical profile of the initial network. We investigate then how to partition a network between measured and unmeasured nodes ensuring that the average of the unmeasured nodes can be efficiently reconstructed. In particular we show that, under hypothesis, this problem can be reduced to a problem of detection of subgraph with particular properties. Methods to achieve this detection are proposed. Finally, three applications are presented: first we apply the partitioning algorithm inducing scale-freeness to a large-scale urban traffic network. We show then that, thanks to the properties preserved through the partition, the reduced network can be used as an abstraction of the initial network. The second and third applications deal with network epidemics. First, we show that the scale-freeness of the abstracting network can be used to build a cure-assignation strategy. In the last application, we take advantage of the result on average reconstruction to estimate the evolution of a disease on a large-scale network.
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https://hal.archives-ouvertes.fr/tel-02532058
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Submitted on : Friday, July 17, 2020 - 11:26:01 AM
Last modification on : Tuesday, October 20, 2020 - 4:59:59 AM

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  • HAL Id : tel-02532058, version 3

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Nicolas Martin. Network partitioning algorithms with scale-free objective. Automatic Control Engineering. Université Grenoble Alpes [2020-..], 2020. English. ⟨NNT : 2020GRALT001⟩. ⟨tel-02532058v3⟩

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