Author: Jean-Guillaume Fages
School: Ecole des Mines de Nantes, LINA, CNRS, INRIA
Supervisors: Xavier Lorca, Nicolas Beldiceanu
Graduated: October 23, 2014
Abstract Many IT applications require to solve decision problems which are hard from a mathematical point of view. Constraint-programming enables to model and solve some of these problems. Among them, some are defined over graphs. Beyond the difficulty stemming from each of these problems, the size of the instance to solve increases the difficulty of the task. This PhD thesis is about the use of graphs within constraint- programming, in order to improve its scalability. First, we study the use of constraint-programming to solve some graph problems involving the computation of trees and Hamiltonian paths and cycles. These problems are important and can be found in many industrial applications. Both filtering and search are investigated. Next, we move on problems which are no longer defined in terms of graph properties. We then study the use of graphs to propagate global constraints. In particular, we suggest a generic schema, relying on a graph structure, to dynamically decompose filtering algorithms. The central theme in this work is the use of graph concepts at the origin of every reasoning and the practical will to increase the size of problems that can be addressed in constraint-programming.
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