done?

beamerthemePoster.sty

@@ -6,12 +6,12 @@
 
 \ProvidesPackage{beamerthemePoster}
 
-
+\RequirePackage[dvipsnames]{xcolor}
-\RequirePackage{tikz}
+% \RequirePackage{tikz}
-\usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,calc}
+% \usetikzlibrary{arrows,decorations.pathmorphing,backgrounds,calc}
 % \RequirePackage{lmodern}
 % \RequirePackage{textcomp}
-% \RequirePackage{amsmath,amssymb}
+\RequirePackage{amsmath,amssymb,amsthm}
 % \usefonttheme{professionalfonts}
 
 \usepackage{ragged2e}
@@ -20,8 +20,11 @@
 %\usepackage{mathptmx}
 % funny math font
 % \usepackage{euler}
-\usepackage[default]{lato}
+\usepackage[defaultsans]{lato}
 \usepackage{lete-sans-math}
+% \RequirePackage[fira]{fontsetup}
+% \RequirePackage{FiraMono}
+% \setmathfont{Fira Math}[range=\setminus]
 
 %%% other text fonts
 %\usepackage{palatino}
@@ -85,16 +88,40 @@
 %set some beamer theme options
   \setbeamertemplate{title page}[default][colsep=-4bp,rounded=true]
   \setbeamertemplate{sections/subsections in toc}[square]
-  \setbeamertemplate{items}[circle]
+  \setbeamertemplate{items}[default]
   \setbeamertemplate{blocks}[width=0.0]
   \beamertemplatenavigationsymbolsempty
 %set bibliography style
- \setbeamertemplate{bibliography item}[text]
+%  \setbeamertemplate{bibliography item}[author]
- \setbeamercolor{bibliography item}{fg=color0,bg=color3}
+%  \setbeamercolor{bibliography item}{fg=color0,bg=color3}
- \setbeamercolor{bibliography entry author}{fg=color0,bg=color3}
+%  \setbeamercolor{bibliography entry author}{fg=color0,bg=color3}
- \setbeamerfont{bibliography item}{size=\small}
+%  \setbeamerfont{bibliography item}{size=\small}
- \setbeamerfont{bibliography entry author}{size=\small}
+%  \setbeamerfont{bibliography entry author}{size=\small}
-
+% theorem env
+\setbeamertemplate{theorem begin}{%
+{
+  \vspace{5pt}%
+  \usebeamerfont*{block title}%
+  \selectfont%
+  \usebeamercolor[fg]{block title}%
+  \textbf{%
+  \inserttheoremname
+  % \inserttheoremnumber
+  \ifx \inserttheoremaddition \empty \else\ \inserttheoremaddition\fi
+  }
+}
+}
+\setbeamertemplate{theorem end}{\vspace{5pt}}
+% proof env
+\setbeamertemplate{proof begin}{%
+{\vspace{5pt}
+\usebeamercolor[fg]{block title}
+\textit{\textbf{Proof:}}}
+}
+\setbeamertemplate{proof end}{
+\qedhere
+\vspace{5pt}
+}
 
 %
 %==============================================================================
@@ -102,9 +129,9 @@
 %==============================================================================
 \setbeamertemplate{headline}{
  \leavevmode
-  \begin{columns}
+  % \begin{columns}
 
-   \begin{column}{\linewidth}
+  %  \begin{column}{\linewidth}
     \vskip2cm
     \centering
     %\usebeamercolor{title in headline}
@@ -115,14 +142,14 @@
     %\usebeamercolor{institute in headline}
 {\color{fg} \large{\insertinstitute}\\[1ex]}
         \vskip2cm
-      \end{column}
+      % \end{column}
       %  \begin{column}{.2\linewidth}
       %    \begin{center}
       %      \includegraphics[width=0.55\linewidth]{image/uestc.png}
       %    \end{center}
       %  \end{column}
       %   \vspace{1cm}
-    \end{columns}
+    % \end{columns}
 
 %%% additional bar under titles
 %\begin{beamercolorbox}[colsep=0.5cm]{colorbar}

ijcai25.tex

@@ -96,9 +96,9 @@
 
 % Please leave this \pdfinfo block untouched both for the submission and
 % Camera Ready Copy. Do not include Title and Author information in the pdfinfo section
-% \pdfinfo{
+\pdfinfo{
-% /TemplateVersion (IJCAI.2025.0)
+/TemplateVersion (IJCAI.2025.0)
-% }
+}
 
 \title{Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints}
 

latexmkrc

@@ -1,2 +1,15 @@
-$pdflatex = 'xelatex %O %S';
 $pdf_mode = 1;
+$pdflatex = 'pdflatex -interaction=nonstopmode %O %S';
+
+# Check the name of the file being compiled.
+# The filename is stored in the first argument, $ARGV[0].
+
+if ( $ARGV[0] =~ /ijcai25\.tex$/i ) {
+    print "--- Found ijcai25.tex, using pdflatex ---\n";
+    $pdf_mode = 1;
+    $pdflatex = 'pdflatex -interaction=nonstopmode %O %S';
+}
+else {
+    $pdf_mode = 4;
+    $pdflatex = 'xelatex -interaction=nonstopmode %O %S';
+}

poster.tex

@@ -8,9 +8,16 @@
   hmargin=2.5cm, % little modification of margins
 }
 \usepackage{lipsum}
+\usepackage{MnSymbol}
+\usepackage{multirow}
+\usepackage{booktabs}
+\usepackage{soul}
+\usepackage{graphicx}
+\usepackage{natbib}
+\usepackage{bibentry}
+% \usepackage{hyperref}[colorlinks=true,urlcolor=Blue,citecolor=Green,linkcolor=BrickRed,unicode]
 
-%
+\DeclareMathOperator*{\conv}{conv}
-\usepackage[utf8]{inputenc}
 
 \linespread{1.15}
 %
@@ -21,10 +28,10 @@
 \title
 [34th International Joint Conference on Artificial Intelligence (IJCAI25), Guangzhou, China] % Conference
 { % Poster title
-\#2001 Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints
+\#2001 \; Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints
 }
 
-\author{\underline{Yu Cong}, Chao Xu, Yi Zhou}
+\author{\texorpdfstring{\underline{Yu Cong}}{Yu Cong}, Chao Xu, Yi Zhou}
 \institute[UESTC]{University of Electronic Science and Technology of China}
 
 \date{\today}
@@ -34,19 +41,147 @@
 \begin{document}
 
 % larger font
-\Large
+\large
 
 \begin{frame}[t]
 \begin{multicols}{2}
 
-  \section{problem}
+\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 $E_i$.
 
+\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 $X\cap E_i\in \mathcal F_i$.
+}
 
+This problem is NP-hard. Consider its LP relaxation.
+\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}
+\textbf{Output}: The entire curve $\tau(B)$ for $B\in [0,\infty)$.
 
+We consider 3 cases of additional constraints $x_{E_i}\in \mathcal{F}_i$ :
+\begin{enumerate}
+\item Multiple-choice. $\sum\limits_{e\in E_i}x_e\leq 1$;
+\item Cardinality. $\sum\limits_{e\in E_i}x_e\leq p$;
+\item Matroid. $x_{E_i}\in \text{independence polytope of a matroid}$.
+\end{enumerate}
 
+\section{Existing works \& Comparison}
 
+\begin{table}[!htb]
+\centering
+\small
+    \begin{tabular}{cccc}
+         Constraint Type & Result & Fixed budget & Trade-off curve \\
+         \bottomrule
+         \hline
+         \multirow{3}{*}{Multiple Choice}& \cite{Dyer84,ZEMEL1984123}& $O(m)$ & -  \\
+         &\cite{10.1109/ITSC55140.2022.9922143} & - & $O(m\log m)$ \\
+         & \textcolor{OrangeRed}{this paper} & - & $O(m\log m)$ \\
+         \hline
+         \multirow{4}{*}{Cardinality}& \cite{DavidPisinger} & $O(m\log VC)$  & -\\
+           & \cite{DavidPisinger} & $O(mp+nB)$  & -  \\
+          & \cite{minimaxoptimization} & $O(m\log m)$  & -  \\
+          & \textcolor{OrangeRed}{this paper} & - & $O((k+m)\log m)$ \\
+         \hline
+         \multirow{3}{*}{Matroid}& \cite{CAMERINI1984157} & $O(m^2 + T \log m)$ & -\\
+        & \cite{minimaxoptimization} & $O(T \log m)$ & - \\
+        & \textcolor{OrangeRed}{this paper} & - & $O(Tk+k\log m)$\\
+        \bottomrule
+    \end{tabular}
+\caption{Comparison of algorithms for incentive allocation: $m$ is the total number of incentives, $M$ is the maximum number of incentives over each agent, $p$ is the max rank of the matroid constraint over each agent, or the limit in the cardinality constraint. $V$ and $C$ is the maximum value and cost of the incentives, respectively. $B$ is the budget. $k=O(mp^{1/3})$ is the number of breakpoints of the trade-off curve. $T$ is the time complexity of matroid optimum base algorithm.}
+\label{runtimetable}
+\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.
+
+\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}
+\label{eq:Lagrangiandual}
+\begin{aligned}
+\min_{\lambda} \left( B\lambda+\sum_i f_i(\lambda)\right).
+\end{aligned}
+\end{equation}
+
+\begin{theorem}[4]\large
+$\tau(B)$ is piecewise-linear and concave.
+\end{theorem}
+
+Computing $\tau(B)$ is straightforward if $f_i(\lambda)$ is known.
+
+\subsection{Finding $f_i(\lambda)$}
+\textcolor{DarkOrchid}{\textit{Cardinality constraint.}}
+For fixed $\lambda$, computing $f_i(\lambda) = \max\{(v_{E_i}-\lambda c_{E_i})x \mid \mathbf{1}\cdot x \leq p\}$ is the same as finding the $p$ largest coupons with respect to the weights $v_e - \lambda c_e$. If $\lambda$ is not fixed, this is computing the \emph{$k$-level} of univariate linear functions.
+\begin{figure}[htb]
+    \begin{minipage}[c]{0.6\linewidth} % Minipage for the image
+        \centering
+        \includegraphics[width=\linewidth]{image/klevel_black.pdf} % Replace with your image
+    \end{minipage}
+    \hfill % Optional: Adds horizontal space between minipages
+    \begin{minipage}[c]{0.39\linewidth} % Minipage for the caption
+        \caption{The bold line forms a $2$-level in the line arrangement.}
+        \label{fig:klevel}
+    \end{minipage}
+\end{figure}
+
+\textcolor{DarkOrchid}{\textit{Matroid constraint.}}
+For fixed $\lambda$ under matroid constraints, computing the signature function is equivalent to finding the optimum-weight base in a matroid.
+However, the matroid generalization of $k$-level problem is significantly harder. We use Eisner-Severance method to compute the curve.
+\section{Computational results}
+
+\begin{table}[!ht]
+\small
+    \centering
+    \begin{tabular}{ccccccccc}
+        \toprule
+         \multirow{2}*{$m$} & \multicolumn{2}{c}{$p=20$} & \multicolumn{2}{c}{$p=40$} &  \multicolumn{2}{c}{$p=2000$} & \multicolumn{2}{c}{$p=m/5$}\\
+         \cmidrule(lr){2-3}  \cmidrule(lr){4-5} \cmidrule(lr){6-7} \cmidrule(lr){8-9}
+         & scan & opt & scan & opt & scan & opt & scan & opt\\
+         \midrule
+        $1\times 10^3$            & 0.000 & 0.000 & 0.000 & 0.001 & - & - & 0.003& 0.002 \\
+        $5\times 10^3$    & 0.003 & 0.005 & 0.006 & 0.005 & 0.137 & 0.027 & 0.091& 0.02\\
+        $1\times 10^4$            & 0.008 & 0.010 & 0.014 & 0.012 & 0.384 & 0.048 & 0.384 & 0.048\\
+        $5\times 10^4$    & 0.043 & 0.089 & 0.080 & 0.087 & 2.634 & 0.187 & 9.531& 0.326\\
+        $1\times 10^5$            & 0.094 & 0.216 & 0.173 & 0.223 & 5.795 & 0.397 & 38.275& 1.222\\
+        $5\times 10^5$    & 0.528 & 2.911 & 0.937 & 2.952 & 33.760 & 3.398 & TLE & 10.500 \\
+        $1\times 10^6$            & 1.147 & 7.291 & 1.989 & 7.140 & 72.485 & 7.604 & TLE & 23.203\\
+        $1\times 10^7$            & 12.994 & 100.512 & 23.863 & 101.675 & TLE & 101.775 & TLE & 133.974\\
+        
+    %     \bottomrule
+    % \end{tabular}
+    % \begin{tabular}{ccccc}
+    %     % \toprule
+    %      \multirow{2}*{$m$} & \multicolumn{2}{c}{$p=2000$} & \multicolumn{2}{c}{$p=m/5$}\\
+    %      \cmidrule(lr){2-3}  \cmidrule(lr){4-5} 
+    %      & scan & opt & scan & opt \\
+    %      \midrule
+    %     $1\times 10^3$      & - & - & 0.003& 0.002 \\
+    %     $5\times 10^3$      & 0.137 & 0.027 & 0.091& 0.02\\
+    %     $1\times 10^4$      & 0.384 & 0.048 & 0.384 & 0.048\\
+    %     $5\times 10^4$      & 2.634 & 0.187 & 9.531& 0.326\\
+    %     $1\times 10^5$      & 5.795 & 0.397 & 38.275& 1.222\\
+    %     $5\times 10^5$      & 33.760 & 3.398 & TLE & 10.500 \\
+    %     $1\times 10^6$      & 72.485 & 7.604 & TLE & 23.203\\
+    %     $1\times 10^7$      & TLE & 101.775 & TLE & 133.974\\
+        
+        \bottomrule
+    \end{tabular}
+    \caption{The time (in seconds) to compute the breakpoints on the signature function under cardinality constraint using the optimum $p$-level algorithm (opt) and the scan line algorithm (scan).}
+    \label{tab:klevel}
+\end{table}
+
+\bibliographystyle{plainnat}
+\nobibliography{ijcai25}
 \end{multicols}
 \end{frame}
 \end{document}