Solving Constrained Graph Problems using Reachability Constraints based on Transitive Closure and Dominators

To my wife, my parents and Fray Luis Amigó y Ferrer Acknowledgments The fulfillment of this thesis would not have been possible without the contribution of: • Peter Van Roy, my supervisor, who gave me the opportunity to work as a research assistant at Université Catholique de Louvain (UCL) from July 2001 until April 2005 in the MISURE project. The goal of the project was the development of a system capable of automatically managing the mission of an uninhabited air vehicle, which was expected to perform a mission in hostile territory almost without the support of human operators. The constrained paths problems involved in this project motivated the research presented in this thesis. • Yves Deville, who kindly accepted to co-supervise my thesis. His pragmatic aptitude and his long experience in constraint programming were essential in narrowing down the scope of the thesis and focusing on the fundamental issues. He also gave me the opportunity to work as a teaching assistant at UCL from October 2005 until August 2006. • Camilo Rueda, who supervised my B.Sc. thesis and let me join his research group at Pontificia Universidad Javeriana in 1996. Even though Camilo was not directly involved in the work of my Ph.D. thesis, the research I carried out under his supervision initiated me into the field of constraint programming. • Raphaël Collet, my genius colleague at UCL. The long discussions that we had were fundamental in helping me understand the concepts underlying my research. • Kevin Glynn, my English colleague at UCL. Apart from helping me with my English, his critical comments let me present my ideas in a more clear way. I must also say that Kevin's advice was of great help when the end of my thesis was not so certain. • Stefano Gualandi, my colleague in MISURE. The good results that we got in MISURE would not have been possible without Stefano. The fact that we were working on the same project provided us with lots of opportunities to interchange ideas. i ii Acknowledgments • Fred Spiessens, a very open minded colleague. The discussions I had with Fred led us to a nice application of the techniques presented in this thesis to the field of Computer Security. • Grégoire Dooms and Stephane Zampelli, who helped me in porting my Oz code to Gecode(CP(Graph)). I appreciate their patience in dealing with my naive questions. • Eugene Ressler, …