z

.gitea/workflows/compile.yml

@@ -7,19 +7,19 @@ jobs:
 
     steps:
       - name: Check out the repository
-        uses: actions/checkout@v4
+        uses: http://localhost:3000/sxlxc/checkout@v4
 
       - name: Compile LaTeX using local TeX Live
         # These commands run directly in your machine's shell
         run: |
           echo "Compiling document..."
-          latexmk -pdf poster.tex
-          latexmk -pdf slides.tex
+          latexmk poster.tex -pdf 
+          latexmk slides.tex -pdf 
       
       - name: List files in the workspace
         run: ls -l
 
-      - uses: akkuman/gitea-release-action@v1
+      - uses: http://localhost:3000/sxlxc/gitea-release-action@v1
         with:
           body: ''
           prerelease: true

beamerthemePoster.sty

@@ -7,8 +7,8 @@
 \ProvidesPackage{beamerthemePoster}
 
 \RequirePackage[dvipsnames]{xcolor}
-% \RequirePackage{tikz}
-% \usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,calc}
+\RequirePackage{tikz}
+\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,calc}
 % \RequirePackage{lmodern}
 % \RequirePackage{textcomp}
 \RequirePackage{amsmath,amssymb,amsthm}
@@ -185,7 +185,7 @@
   \end{center}
 \end{minipage}
   \end{center}
-    \vskip1cm
+    \vskip0.8cm
 }
 
 %
@@ -195,11 +195,11 @@
 \renewcommand{\section}[1]{
 \par\vskip\medskipamount%
 %
-    %  \begin{flushleft}
-    %  \begin{tikzpicture}[remember picture,overlay]
-    %    \shade [inner color=color2,outer color=color3] (0,0) rectangle (\columnwidth,0.3cm);
-    %  \end{tikzpicture}
-    %  \end{flushleft}
+     \begin{flushleft}
+     \begin{tikzpicture}[remember picture,overlay]
+       \shade [inner color=color2,outer color=color3] (0,0) rectangle (\columnwidth,0.3cm);
+     \end{tikzpicture}
+     \end{flushleft}
     % \vspace{5pt}
 %
      \begin{center}
@@ -208,12 +208,12 @@
      {\parskip0pt\par}
      \end{center}
 %
-    %  \begin{flushleft}
-    %  \vskip-1cm
-    %  \begin{tikzpicture}[remember picture,overlay]
-    %    \shade [inner color=color2,outer color=color3] (0,0) rectangle (\columnwidth,0.3cm);
-    %  \end{tikzpicture}
-    %  \end{flushleft}
+     \begin{flushleft}
+     \vskip-1cm
+     \begin{tikzpicture}[remember picture,overlay]
+       \shade [inner color=color2,outer color=color3] (0,0) rectangle (\columnwidth,0.3cm);
+     \end{tikzpicture}
+     \end{flushleft}
     % \vspace{2.5pt}
 %
   {\parskip0pt\par}

poster.tex

@@ -39,31 +39,31 @@
 
 
 \begin{document}
-
 % larger font
 \large
 
 \begin{frame}[t]
+\vspace{-3cm}
 \begin{multicols}{2}
 
 \section{Problem}
 We consider the incentive allocation problem with additional constraints.
 
-\textbf{Input}: A set of coupons $E=\bigcupdot_i E_i$, where each coupon $e\in E$ has value and cost $v_e,c_e\in \mathbb{Z}_+$. Budget $B\in \mathbb{Z}_+$. Constraints $\mathcal F_i$ on each subset $E_i$.
+\textbf{Input}: A set of coupons $E=\bigcupdot_i E_i$, where each coupon $e\in E$ has a value and a cost $v_e,c_e\in \mathbb{Z}_+$. Budget $B\in \mathbb{Z}_+$. Constraints $\mathcal F_i$ on each subset $E_i$.
 
 \textcolor{Gray}{
-\textbf{Output}: A subset $X\subset E$ of coupons that maximizes the total value $\sum_{e\in X}v_e$ while satisfying $\sum_{e\in X}c_e\leq B$ and additional constraints $X\cap E_i\in \mathcal F_i$.
+\textbf{Output}: A subset $X\subset E$ of coupons that maximizes the total value $\sum_{e\in X}v_e$ while satisfying the budget constraint $\sum_{e\in X}c_e\leq B$ and additional constraints $X\cap E_i\in \mathcal F_i$.
 }
 
 This problem is NP-hard. Consider its LP relaxation.
-\begin{equation}\label{LP}
+\begin{equation*}\label{LP}
 \begin{aligned}
 \tau(B)=\max_x&\; & v\cdot x& & & \\
 s.t.&\;  & c \cdot x &\leq B & &\\
 & & x_{E_i}&\in \conv(\mathcal{F}_i)  & &\;\forall i\in [n]\\
 & & x&\in [0,1]^m & &
 \end{aligned}
-\end{equation}
+\end{equation*}
 \textbf{Output}: The entire curve $\tau(B)$ for $B\in [0,\infty)$.
 
 We consider 3 cases of additional constraints $x_{E_i}\in \mathcal{F}_i$ :
@@ -101,17 +101,17 @@ We consider 3 cases of additional constraints $x_{E_i}\in \mathcal{F}_i$ :
 \end{table}
 
 \section{Methods}
-The idea is to take advantage of the independence among the constraints $\mathcal{F}_i$ and to reduce the optimization problem to one in computational geometry.
+The idea is to take advantage of the independence among the constraints $\mathcal{F}_i$ and reduce the optimization problem to one in computational geometry.
 
 \textcolor{DarkOrchid}{\textit{Signature Function.}} Let $f_i(\lambda) = \max\{(v_{E_i}-\lambda c_{E_i}) x | x\in \conv(\mathcal F_i) \}$ be the signature function of agent $i$. The signature function is piecewise-linar and convex.
 
 \textcolor{DarkOrchid}{\textit{Lagrangian Dual.}} The Lagrangian dual of LP\autoref{LP} is therefore
-\begin{equation}
+\begin{equation*}
 \label{eq:Lagrangiandual}
 \begin{aligned}
 \min_{\lambda} \left( B\lambda+\sum_i f_i(\lambda)\right).
 \end{aligned}
-\end{equation}
+\end{equation*}
 
 \begin{theorem}[4]\large
 $\tau(B)$ is piecewise-linear and concave.

slides.tex

@@ -4,6 +4,15 @@
 \usepackage{algo}
 \usepackage{soul}
 % \usepackage{cancel}
+\newcommand{\munepsfig}[3][scale=1.0]{% <===============================
+    \begin{figure}[!htbp]
+        \centering
+        \vspace{2mm}
+        \setlength{\fboxrule}{#3} % <===================================
+        \framebox{\includegraphics[#1]{#2.png}} % <=====================
+        \label{fig:#2}
+    \end{figure}
+}
 
 \title[Incentive allocation]{Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints}
 \date{August 30, 2025}
@@ -28,8 +37,9 @@ A ride sharing company wants to send riders promotional coupons in the hope of m
 
 %  each agent gets at most 1 coupon.
 \begin{figure}
-placeholder\\
-\includegraphics[width=.5\textwidth]{image/landscape.png}
+\includegraphics[width=.7\textwidth]{image/chatgpt.png}
+
+\scriptsize Image courtesy: ChatGPT-5
 \end{figure}
 
 \end{frame}
@@ -37,24 +47,24 @@ placeholder\\
 \begin{frame}{Multiple-choice knapsack}
 \textbf{Input}: $n$ sets of coupons $K_1,\dots,K_n$. Each coupon $e\in K_i$ has a non-negative cost $c_e\in \Z_+$ and value $v_e\in \Z_+$. A positive budget $b\in \Z_+$.
 
-\textbf{Output}: A (multi)set of coupons $K$ that maximizes the total value $\sum_{e\in K} c_e$ while satisfying \textcolor{Red}{$|K\cap K_i|\leq 1$} and $\sum_{e\in K} c_e\leq b$.
+\textbf{Output}: A subset of coupons $K$ that maximizes the total value $\sum_{e\in K} v_e$ while satisfying \textcolor{Red}{$|K\cap K_i|\leq 1$} and $\sum_{e\in K} c_e\leq b$.
 
 \vspace{1em}
 \pause
 
-Three problems with this modeling:
+Three problems with this formulation:
 \begin{enumerate}
 \item Finding the exact optimum is NP-hard. So we consider solving it approximately.
 \item Companies may run multiple campaigns at the same time. So a trade-off curve between budget and profit will be useful.
-\item The multiple-choice constraint \textcolor{Red}{$|K\cap K_i|\leq 1$} is too weak for real applications.
+\item The multiple-choice constraint \textcolor{Red}{$|K\cap K_i|\leq 1$} is too strong for real-world applications.
 \end{enumerate}
 
 \end{frame}
 
-\begin{frame}{Linear programming formulation}
-\textcolor{gray}{
+\begin{frame}{Linear programming relaxation}
+% \textcolor{gray}{
 \textbf{Input}: $n$ sets of coupons $K_1,\dots,K_n$. Each coupon $e\in K_i$ has a non-negative cost $c_e\in \Z_+$ and value $v_e\in \Z_+$. \st{A positive budget $b\in \Z_+$.}
-}
+% }
 \pause
 \begin{equation*}
 \begin{aligned}
@@ -64,7 +74,7 @@ s.t.&   &   c\cdot x&\leq b     &   &\\
 \end{aligned}
 \end{equation*}
 
-\textbf{Output}: A compact representation of $\tau(b)$.
+\textbf{Output}: function $\tau(b)$ for $b\in (0,+\infty)$.
 \pause
 
 We focus on 2 kinds of constraints of \textcolor{Plum}{$x_{K_i}\in P_{K_i}$}.
@@ -88,6 +98,12 @@ $k=O(mp^{1/3})$ and $\tau$ can be computed in $O((k+m)\log m)$ time.
 \end{frame}
 
 \begin{frame}[plain]
-poster
+\centering
+\Large \textit{Let's discuss this in detail at my poster!}
+
+\munepsfig[width=.8\linewidth]{image/poster}{1pt}
+% \begin{figure}
+% \includegraphics[width=0.8\linewidth]{image/poster.png}
+% \end{figure}
 \end{frame}
 \end{document}