--- a/minimum_bisection/presentation.tex	Tue May 20 22:09:58 2014 +0200
+++ b/minimum_bisection/presentation.tex	Tue May 20 22:37:17 2014 +0200
@@ -20,7 +20,7 @@
             \item A \structure{capacity function} $c : E \to \R^+$
             \item A source $s$ and a target $t$
         \end{itemize}
-        \uncover<4->{Calculate the maximum possible \structure{flow} $f : E \to \R^+$ through $G$.}
+        \uncover<4->{Calculate a maximum possible \structure{flow} $f : E \to \R^+$ through $G$.}
     \end{problem}
 
     \centering
@@ -45,7 +45,7 @@
             \item A capacity function $c : E \to \R^+$
             \item<2-> A \structure{demand function} $d : V^2 \to \R^+$
         \end{itemize}
-        \uncover<3->{Calculate the flow $f$ with least \structure{congestion $\rho = \max_{e \in E}\frac{f_e}{c_e}$}.}
+        \uncover<3->{Calculate a flow $f$ with least \structure{congestion $\rho = \max_{e \in E}\frac{f_e}{c_e}$}.}
     \end{problem}
 
     \centering
@@ -331,10 +331,7 @@
     \begin{itemize}
         \item Identify every edge in a tree with a \structure{path} in $G$
         \item These paths can \structure{overlap}
-        \item For tree $T$ we get a mapping $P$
-            \begin{align}
-                P : E_T \to E^+
-            \end{align}
+        \item For tree $T$ we get a mapping $P_T : E_T \to E^+$
     \end{itemize}
 
     \vfill
@@ -405,7 +402,9 @@
         }
 
         \only<4-> {
-            \draw[demand edge, bend left=10] (l) edge node[flow demand, pos=0.2]{9} (i);
+            \begin{pgfonlayer}{demand}
+                \draw[demand edge, bend left=10] (l) edge node[flow demand, pos=0.2]{9} (i);
+            \end{pgfonlayer}
 
             \begin{pgfonlayer}{marked}
                 \foreach \source/ \dest in {l/m,m/e,d/k,k/j,j/i}
@@ -456,7 +455,7 @@
 
     \only<2> {
         \begin{center}
-            \Large How do we find such a set of trees? How large is $\alpha$?
+            How do we find such a set of trees? How large is $\alpha$?
         \end{center}
     }
 \end{frame}
@@ -692,10 +691,10 @@
 
         \draw
             (n) node[above=0.1] {\structure{u}}
-            (m) node[below] {a}
-            (e) node[below] {b}
+            (m) node[below=0.05] {a}
+            (e) node[below=0.05] {b}
             (d) node[above=0.1] {c}
-            (c) node[below] {d}
+            (c) node[below=0.05] {d}
             (b) node[above=0.1] {\structure{v}};
 
         \path
@@ -791,8 +790,8 @@
     \vfill
 
     \begin{itemize}
-        \item There is a $\structure{\lambda}$ such that $\alpha \in \Oh(\log n)$
-        \item So out algorithm as an \alert{$\Oh(\log n)$ approximation}
+        \item There is a $\structure{\lambda}$ such that $\structure{\alpha \in \Oh(\log n)}$
+        \item The algorithm as an \alert{$\Oh(\log n)$-approximation}
         \item But why are polynomially many trees enough?
     \end{itemize}
 \end{frame}