Commit 8e1b833d authored by Simon de Givry's avatar Simon de Givry
Browse files

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}
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\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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