Skip to content
GitLab
Menu
Projects
Groups
Snippets
Help
Help
Support
Community forum
Keyboard shortcuts
?
Submit feedback
Contribute to GitLab
Sign in
Toggle navigation
Menu
Open sidebar
Simon de Givry
enac
Commits
8e1b833d
Commit
8e1b833d
authored
Oct 19, 2020
by
Simon de Givry
Browse files
Merge branch 'master' of
https://forgemia.inra.fr/degivry/enac
parents
c048bd9e
c8073798
Changes
2
Hide whitespace changes
Inline
Side-by-side
Graphe-Slides.pdf
View file @
8e1b833d
No preview for this file type
Graphe-Slides.tex
View file @
8e1b833d
...
...
@@ -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
}
...
...
Write
Preview
Markdown
is supported
0%
Try again
or
attach a new file
.
Attach a file
Cancel
You are about to add
0
people
to the discussion. Proceed with caution.
Finish editing this message first!
Cancel
Please
register
or
sign in
to comment