Binary file minimum_bisection/presentation.pdf has changed

--- a/minimum_bisection/presentation.tex	Wed May 21 22:58:09 2014 +0200
+++ b/minimum_bisection/presentation.tex	Wed May 21 23:12:14 2014 +0200
@@ -213,7 +213,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Optimal solution}
+    \frametitle{Optimal Solution}
 
     \begin{lemma}
         For any tree $T$ and any tree edge $e_T$, we know that for \alert{any routing} in $G$ there must be an edge with \structure{congestion}
@@ -239,7 +239,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Routing with multiple spanning trees}
+    \frametitle{Routing with multiple Spanning Trees}
 
     \begin{itemize}
         \item Choose a \structure{set of spanning trees $\left\{ T_i \right\}$} of $G$
@@ -305,7 +305,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Routing with multiple spanning trees}
+    \frametitle{Routing with multiple Spanning Trees}
 
     \begin{itemize}
         % \item Remember that the total flow on edge $e \in E$ is
@@ -365,7 +365,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Routing with multiple pathtrees}
+    \frametitle{Routing with multiple Pathtrees}
 
     \begin{itemize}
         \item Choose a \structure{set of pathtrees $\left\{ T_i \right\}$} of $G$ with \structure{combination $\lambda$}
@@ -487,7 +487,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Dual program}
+    \frametitle{Dual Program}
 
     \begin{block}{Dual Program}
         Let $\Ih$ be the exponenitally large set of \structure{all pathtrees}.
@@ -507,7 +507,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Solution of the dual}
+    \frametitle{Solution of the Dual Program}
 
     \begin{block}{Dual Program}
         Let $\Ih$ be the exponenitally large set of \structure{all pathtrees}.
@@ -545,7 +545,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Solution of the dual}
+    \frametitle{Solution of the Dual Program}
 
     \begin{block}{Dual Program}
         Let $\Ih$ be the exponenitally large set of \structure{all pathtrees}.
@@ -680,7 +680,7 @@
     \frametitle{Sum over all capacities}
 
     \begin{lemma}[]
-        Let $T$ a spanning tree and $(V, M)$ a tree metric of $G = (V, E)$. Then
+        Let $T$ be a spanning tree and $(V, M)$ a tree metric of $G = (V, E)$. Then
         \begin{align}
             \sum_{(x, y) \in E_T} C(x, y) M_{xy} = \sum_{(u, v) \in E} c_{uv} M_{uv}
         \end{align}
@@ -758,7 +758,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Value of the dual problem}
+    \frametitle{Value of the Dual Problem}
 
     \begin{block}{Dual Program}
         Let $\Ih$ be the exponenitally large set of \structure{all pathtrees}.
@@ -779,7 +779,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Value of the primal program}
+    \frametitle{Value of the Primal Program}
 
     \begin{block}{Primal Program}
         Let $\Ih$ be the exponenitally large set of \structure{all pathtrees}.\\
@@ -796,7 +796,7 @@
 
     \begin{itemize}
         \item There is a $\structure{\lambda}$ such that $\structure{\alpha \in \Oh(\log n)}$
-        \item The algorithm is an \alert{$\Oh(\log n)$-approximation}
+        \item Solving the LP is an \alert{$\Oh(\log n)$-approximation}
         \item But why are polynomially many trees enough?
     \end{itemize}
 \end{frame}
@@ -867,7 +867,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Tree bisections}
+    \frametitle{Tree Bisections}
 
     \begin{itemize}
         \item Given a spanning tree $T$ of $G$ with an edge $e_T \in E_T$
@@ -910,7 +910,7 @@
 \end{frame}
 
 \begin{frame}
-    \frametitle{Tree bisections}
+    \frametitle{Tree Bisections}
 
     \begin{lemma}[]
         For any tree $T$ and any $S \subseteq V$ we have