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Aspects de l’efficacité dans des problèmes sélectionnés pour des calculs sur les graphes de grande taille

Mengchuan Zou 1
1 GANG - Networks, Graphs and Algorithms
IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale, Inria de Paris
Abstract : This thesis presents three works on different aspects of efficiency of algorithm design for large scale graph computations. In the first work, we consider a setting of classical centralized computing, and we consider the question of generalizing modular decompositions and designing time- efficient algorithm for this problem. Modular decomposition, and more broadly module detection, are ways to reveal and analyze modular properties in structured data. As the classical modular decomposition is well studied and have an optimal linear-time algorithm, we firstly study the generalizations of these concepts to hy- pergraphs and present here positive results obtained for three definitions of modular decomposition in hypergraphs from the literature. We also consider the generaliza- tion of allowing errors in classical graph modules and present negative results for two this kind of definitions. The second work focuses on graph data query scenarios. Here the model differs from classical computing scenarios in that we are not designing algorithms to solve an original problem, but we assume that there is an oracle which provides partial information about the solution to the original problem, where oracle queries have time or resource consumption, which we model as costs, and we need to have an algorithm deciding how to efficiently query the oracle to get the exact solution to the original problem, thus here the efficiency is addressing to the query costs. We study the generalized binary search problem for which we compute an efficient query strategy to find a hidden target in graphs. We present the results of our work on approximating the optimal strategy of generalized binary search on weighted trees. Our third work draws attention to the question of memory efficiency. The setup in which we perform our computations is distributed and memory-restricted. Specif- ically, every node stores its local data, exchanging data by message passing, and is able to proceed local computations. This is similar to the LOCAL/CONGEST model in distributed computing, but our model additionally requires that every node can only store a constant number of variables w.r.t. its degree. This model can also describe natural algorithms. We implement an existing procedure of multiplicative reweighting for approximating the maximum s–t flow problem on this model, this type of methodology may potentially provide new opportunities for the field of local or natural algorithms. From a methodological point of view, the three types of efficiency concerns cor- respond to the following types of scenarios: the first one is the most classical one – given the problem, we try to design by hand the more efficient algorithm; the second one, the efficiency is regarded as an objective function – where we model query costs as an objective function, and using approximation algorithm techniques to get a good design of efficient strategy; the third one, the efficiency is in fact posed as a constraint of memory and we design algorithm under this constraint.
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Mengchuan Zou. Aspects de l’efficacité dans des problèmes sélectionnés pour des calculs sur les graphes de grande taille. Algorithme et structure de données [cs.DS]. Université de Paris, 2019. Français. ⟨tel-02436610⟩

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