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Routages optimaux : tours, flots et chemins.

Guyslain Naves 1 
1 G-SCOP_OC - Optimisation Combinatoire
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
Abstract : The study of cycles, flows and paths in graphs is closely related to the development of combinatorial optimization. In the introduction, we explicit this relationship by using classical results, and the two next parts develops new results in two distinct directions. First, we look at problems of existence of integer multiflow. Many parameters can naturally be applied to them. By combination they yield a hundred distinct cases. We present the state of the art in a synthetic way, and then prove some new results. We prove the NP-completeness of finding two disjoint flows in planar graphs. We also give an algorithm for solving multiflow problems in acyclic digraphs with Euler condition, when the number of classes of demand is bounded. Then, we consider the problem of finding a shortest spanning closed walk. More precisely, when does this problem admit a good characterisation based on packing of scattering sets ? We give some polyhedral results, and investigate the case of cographs and interval graphs.
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Submitted on : Friday, March 19, 2010 - 9:52:33 PM
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Guyslain Naves. Routages optimaux : tours, flots et chemins.. Informatique [cs]. Université Joseph-Fourier - Grenoble I, 2010. Français. ⟨tel-00465585⟩

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