Commit 8e1b833d by Simon de Givry

### Merge branch 'master' of https://forgemia.inra.fr/degivry/enac

parents c048bd9e c8073798
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 ... ... @@ -3873,6 +3873,17 @@ On a $c(T) \leq c(H^*)$ \end{block} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{P vs NP} \begin{block}{P} The class of problems we can solve in polynomial time \end{block} \begin{block}{NP} The class of problems for which we can verify a solution in polynomial time \end{block} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{ILP as a modeling language} ... ... @@ -3929,6 +3940,17 @@ On a $c(T) \leq c(H^*)$ \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{The notion of completeness} \begin{itemize} \item ILP is at least as hard as CNFSAT \item If it was at least as hard as \emph{any} problem in NP, we say it is NP-complete \item And it is! \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{Classes and reductions -- informal} ... ... @@ -3954,7 +3976,7 @@ On a $c(T) \leq c(H^*)$ \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{Languages} \begin{frame}{Languages} \begin{block}{Language} A language $\mathcal{L}$ is an infinite set of strings \end{block} ... ... @@ -4032,6 +4054,7 @@ On a $c(T) \leq c(H^*)$ \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \shrink{ \begin{frame}{Computational models} In order to define computational properties, we need an abstract machine model on which we can measure resource use ... ... @@ -4180,6 +4203,7 @@ On a $c(T) \leq c(H^*)$ problems. \end{frame} } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{Algorithmic complexity} ... ... @@ -4220,7 +4244,8 @@ On a $c(T) \leq c(H^*)$ \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{P-Completeness} \shrink{ \begin{frame}{P-Completeness} \begin{block}{Class $P$} Languages recognized in polynomial time in the RAM model \end{block} ... ... @@ -4251,7 +4276,7 @@ On a $c(T) \leq c(H^*)$ connected? \end{block} \end{frame} } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{NP} \begin{block}{Informal definition} ... ... @@ -4389,7 +4414,8 @@ On a $c(T) \leq c(H^*)$ \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{Function Problems} \shrink{ \begin{frame}{Function Problems} \begin{itemize} \item P, NP contain only \emph{decision} problems. Functions belong to $FP$ or $FNP$. ... ... @@ -4434,6 +4460,7 @@ On a $c(T) \leq c(H^*)$ \begin{frame}{Complexity Classes} \includegraphics[width=\textwidth]{complexity-classes} \end{frame} } %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{Dealing with NP-completeness} ... ... @@ -4530,10 +4557,6 @@ On a $c(T) \leq c(H^*)$ Model Hamiltonian Circuit with CSP \end{block} \begin{block}{Exercise} Model TSP with CSP \end{block} \begin{block}{Exercise} Model Vertex Cover with CSP \end{block} ... ... @@ -4561,6 +4584,16 @@ On a $c(T) \leq c(H^*)$ \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{CP Implementations} \begin{itemize} \item Gecode: \href{https://www.gecode.org/}{https://www.gecode.org/} (C++) \item Google OR Tools: \href{https://developers.google.com/optimization}{https://developers.google.com/optimization} (C++) \item Choco: \href{https://choco-solver.org/}{https://choco-solver.org/} (Java) \end{itemize} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{What is a Graphical Model?} ... ... @@ -4687,6 +4720,21 @@ On a $c(T) \leq c(H^*)$ \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame} \frametitle{Modeling with Graphical Models} \begin{block}{Exercise} Model MaxCut with WCSP \end{block} \begin{block}{Exercise} Model TSP with WCSP \end{block} \end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \shrink{ \begin{frame}{Stochastic Graphical Models} ... ...
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