z

slides.tex

@@ -60,7 +60,7 @@ Three problems with this modeling:
 \begin{aligned}
 \tau(b)= \max_x&    &   v\cdot x&   &   &\\
 s.t.&   &   c\cdot x&\leq b     &   &\\
-&   &       \textcolor{Plum}{x_{K_i}}&\textcolor{Plum}{\in P_{K_i}} &   &\forall i\in [n]\\
+&   &       \mathcolor{Plum}{x_{K_i}}&\mathcolor{Plum}{\in P_{K_i}} &   &\forall i\in [n]\\
 \end{aligned}
 \end{equation*}
 
@@ -78,7 +78,7 @@ We focus on 2 kinds of constraints of \textcolor{Plum}{$x_{K_i}\in P_{K_i}$}.
 We compute the curve $\tau(b)$ fast.
 \begin{theorem}
 Consider an incentive allocation problem with a total of $m$ incentives. 
-The trade-off curve is piecewise linear concave function with $k$ breakpoints.
+The trade-off curve is a piecewise linear concave function with $k$ breakpoints.
 \begin{itemize}
 \item Cardinality constraint.
 $k=O(mp^{1/3})$ and $\tau$ can be computed in $O((k+m)\log m)$ time.