\select@language {french}
\contentsline {part}{I\hspace {1em}G\IeC {\'e}n\IeC {\'e}ration de carte routi\IeC {\`e}re r\IeC {\'e}aliste}{2}
\contentsline {section}{\numberline {1}Condition pour un graphe de Gabriel}{2}
\contentsline {paragraph}{preuve :}{2}
\contentsline {section}{\numberline {2}Mise en pratique : graphe de Gabriel et de voisinage relatif}{2}
\contentsline {subsection}{\numberline {2.1}Cr\IeC {\'e}ation de graphe de Gabriel et de voisinage relatif}{2}
\contentsline {subsection}{\numberline {2.2}G\IeC {\'e}n\IeC {\'e}ration d'un r\IeC {\'e}seau}{2}
\contentsline {subsection}{\numberline {2.3}Temps de g\IeC {\'e}n\IeC {\'e}ration d'un r\IeC {\'e}seau}{6}
\contentsline {section}{\numberline {3}Triangulation de Delaunay}{6}
\contentsline {subsection}{\numberline {3.1}Pratique}{6}
\contentsline {subsection}{\numberline {3.2}Aspect th\IeC {\'e}orique}{6}
\contentsline {subsubsection}{\numberline {3.2.1}Condition pour un graphe de Delaunay}{6}
\contentsline {paragraph}{preuve:}{6}
\contentsline {subsubsection}{\numberline {3.2.2}Le graphe de Delaunay est planaire}{7}
\contentsline {paragraph}{preuve}{7}
\contentsline {subsubsection}{\numberline {3.2.3}Le graphe de Delaunay est une triangulation}{7}
\contentsline {paragraph}{preuve}{7}
\contentsline {subsubsection}{\numberline {3.2.4}Condition sur les faces}{8}
\contentsline {paragraph}{preuve}{8}
\contentsline {part}{II\hspace {1em}Algorithme de Dijkstra pour la recherche du plus court chemin}{9}
\contentsline {section}{\numberline {4}Algorithme de Dijkstra}{9}
\contentsline {subsection}{\numberline {4.1}Co\IeC {\^u}ts constants}{9}
\contentsline {subsection}{\numberline {4.2}Co\IeC {\^u}ts variables}{9}
\contentsline {subsection}{\numberline {4.3}Temps de calcul}{9}
\contentsline {section}{\numberline {5}Dijkstra avec tas}{9}
\contentsline {section}{\numberline {6}Algorithme A*}{9}
\contentsline {part}{III\hspace {1em}Probl\IeC {\`e}me du voyageur de commerce}{13}
\contentsline {section}{\numberline {7}R\IeC {\'e}solution par Backtracking}{13}
\contentsline {subsection}{\numberline {7.1}R\IeC {\'e}solution}{13}
\contentsline {subsection}{\numberline {7.2}Temps d'ex\IeC {\'e}cution}{13}
\contentsline {section}{\numberline {8}R\IeC {\'e}solution approch\IeC {\'e}e}{13}