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Résolution du problème du p-médian, application à la restructuration de bases de données semi-structurées

Abstract : The problems we consider in this thesis are of combinatorial nature. Our main interest is the problem of approximating typing of a semistructured data. For example XML is a semistructured data. This problem may be reduced to an instance of the p-median problem. The main obstacle here is the size of the instances that may be very huge, about 10000 and 20000 nodes which imply several hundreds of million variables. For these instances, even solving the linear relaxation is a hard task. In some preliminary results we noticed that Cplex may solve instances of size 1000 in an acceptable time. But for some instances having 5000 nodes, it may needs 14 days for solving only the linear relaxation. Therefore, we cannot use methods that consider the linear relaxation as an elementary operation, as for example branch-and-cut methods. Instead of using Cplex we use the Volume algorithm in a parallel implementation (32 processors).For the instance where the Cplex needs 14 hours, the Volume algorithm in sequential implementation needs 24 minutes and in parallel implementation it needs 10 minutes. The solution of the linear relaxation is used to produce a feasible solution by first applying a greedy and then a local search heuristic. We notice that the results we obtain are relatively the same as those given by the best method known up today, which produces more effort and consumes more memory. Memory is important in our case since the data we consider are huge. We study the dominant of the polytope associated with the p-median problem. We discuss linear relaxation and a polyhedral characterization. Finally, we consider a more realistic version of the p-median problem when applied to the problem of approximating typing of a semistructured data. Roughly speaking, we add new nodes to the underlying graph if this help to reduce the overall cost.
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Jean-Christophe Gay. Résolution du problème du p-médian, application à la restructuration de bases de données semi-structurées. Autre [cs.OH]. Université Blaise Pascal - Clermont-Ferrand II, 2011. Français. ⟨NNT : 2011CLF22171⟩. ⟨tel-00720204⟩

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