Contraintes de Partitionnement de Graphe

Abstract : Combinatorial problems based on graph partitioning enable to represent many practical applications. Examples based on phylogenetic supertree problem, mission planning, or the routing problems in logistic, perfectly illustrate such applications. Nevertheless, these problems are not based on the same partitioning pattern : Generally, patterns like cycles, paths, or trees are distinguished. Moreover, the practical applications are not often limited to theoretical problems like Hamiltonian path problem, or K-node disjoint paths problems. Indeed, they usually combine the graph partitioning problem with several restrictions related to the topology of nodes and arcs. The diversity of implied constraints in real-life applications is a practical limit to the resolution of such problems by approaches considering the partitioning problem independently from each additional restriction. This thesis focuses on constraint satisfaction problems related to tree partitioning problems enriched by several additional constraints that restrict the possible partitions topology. On the one hand, our study focuses the structural properties of tree partitioning constraints. On the ohter hand, it is dedicated to the interactions between the tree partitioning problem and classical restrictions (such as precedence relations or incomparability relations between nodes) involved in practical applications. Precisely, we show how to globally take into account several restrictions within one single tree partitioning constraint. Another interesting aspect of this thesis is related to the implementation of such a constraint. In the context of graph-based global constraints, we show how a fully dynamic management of data structures makes the runtime of filtering algorithms independent of the graph density.
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Xavier Lorca. Contraintes de Partitionnement de Graphe. Autre [cs.OH]. Université de Nantes, 2007. Français. ⟨tel-00484354⟩

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