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Yu Cong
2025-08-20 17:33:22 +08:00
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beamerthemePoster.sty
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% \shade [inner color=color2,outer color=color3] (0,0) rectangle (\columnwidth,0.3cm);
% \end{tikzpicture}
% \end{flushleft}
\vspace{5pt}
% \vspace{5pt}
%
\begin{center}
%\vskip1cm
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% \shade [inner color=color2,outer color=color3] (0,0) rectangle (\columnwidth,0.3cm);
% \end{tikzpicture}
% \end{flushleft}
\vspace{5pt}
% \vspace{2.5pt}
%
{\parskip0pt\par}
\justifying

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beamerthemeSlides.sty
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\else%
\hskip12pt%
\fi%
\insertsubsectionhead\hfill\insertshortauthor\hskip12pt\insertframenumber/\inserttotalframenumber\hspace{0.5em}
\insertsubsectionhead\hfill\insertshortauthor\hskip6pt\insertshortinstitute\hskip12pt\insertframenumber/\inserttotalframenumber\hspace{0.5em}
\end{beamercolorbox}
\begin{beamercolorbox}[wd=\paperwidth,colsep=1.5pt]{lower separation line head}
\end{beamercolorbox}
@@ -123,7 +123,7 @@
% item settings
\setbeamertemplate{itemize item}{$\color{beamer@simple@color}\bullet$}
\setbeamertemplate{itemize subitem}{$\color{beamer@simple@color}\bullet$}
\setbeamertemplate{enumerate items}[square]
\setbeamertemplate{enumerate items}[default]
\setbeamertemplate{section in toc}[sections numbered]
\setbeamertemplate{subsection in toc}[square]

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poster.tex
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%==Title, date and authors of the poster=======================================
\title
[IJCAI25, 29 - 31 August 2025, Guangzhou, China] % Conference
[34th International Joint Conference on Artificial Intelligence (IJCAI25), 29 - 31 August 2025, Guangzhou, China] % Conference
{ % Poster title
Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints
}
@@ -36,6 +36,10 @@ Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinalit
\begin{document}
% larger font
\Large
\begin{frame}[t]
%==============================================================================
\begin{multicols}{2}
@@ -45,78 +49,7 @@ Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinalit
\section{Introduction}
\lipsum
\begin{equation}
H = \sum_{i=1}^{N} h_{D}(i) + \sum_{j>i=1}^{N} C_{ij}
\end{equation}
In Ref.~\cite{ref1}...
In Refs.~\cite{ref1,ref2}...
On webpage~\cite{web}...
\section{Result and discussions}
\vskip1ex
\begin{table}
\centering
\caption{This is a table with scientific results.}
\begin{tabular}{ccccc}
\hline\hline
1 & 2 & 3 & 4 & 5\\
\hline
aaa & bbb & ccc & ddd & eee\\
aaaa & bbbb & cccc & dddd & eeee\\
aaaaa & bbbbb & ccccc & ddddd & eeeee\\
aaaaaa & bbbbbb & cccccc & dddddd & eeeeee\\
1.000 & 2.000 & 3.000 & 4.000 & 5.000\\
\hline\hline
\end{tabular}
\end{table}
\vskip2ex
blabla
\vskip1ex
\begin{figure}
\centering
\includegraphics[width=0.99\columnwidth]{./image/landscape.png}
\caption{This is a picture with scientific results.}
\end{figure}
\vskip2ex
sdfsdf
\subsection{SubSection, a very very very very very very long title}
sdfsdf
\section{Summary and conclusions}
\lipsum[1-3]
%==============================================================================
%==End of content==============================================================
%==============================================================================
%--References------------------------------------------------------------------
\subsection{References}
\begin{thebibliography}{99}
\bibitem{ref1} J.~Doe, Article name, \textit{Phys. Rev. Lett.}
\bibitem{ref2} J.~Doe, J. Smith, Other article name, \textit{Phys. Rev. Lett.}
\bibitem{web} \url{http://www.google.pl}
\end{thebibliography}
%--End of references-----------------------------------------------------------
\lipsum[1-7]
\end{multicols}

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slides.tex
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\usetheme{Slides}
\usepackage{algo}
\usepackage{soul}
% \usepackage{cancel}
\title[Incentive allocation]{Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints}
\date{\today}
\date{August 30, 2025}
\author{\underline{Yu Cong}, Chao Xu, Yi Zhou}
\institute[UESTC]{University of Electronic Science and Technology of China}
% \AtBeginSection[]{
@@ -17,9 +18,76 @@
\begin{document}
\begin{frame}[plain]
\titlepage
\scriptsize 34th International Joint Conference on Artificial Intelligence (IJCAI25)
\end{frame}
\begin{frame}{title ggg fff}
\ul{sdfggg}
% introduce the problem. 3 things: trade-off curve, approximation, general constraints
\begin{frame}{Incentive allocation with constraints}
A ride sharing company wants to send riders promotional coupons in the hope of more rides.
% each agent gets at most 1 coupon.
\begin{figure}
placeholder\\
\includegraphics[width=.5\textwidth]{image/landscape.png}
\end{figure}
\end{frame}
\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 $\sum_{e\in K} c_e\leq b$.
\vspace{1em}
\pause
Three problems with this modeling:
\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.
\end{enumerate}
\end{frame}
\begin{frame}{Linear programming formulation}
\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}
\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]\\
\end{aligned}
\end{equation*}
\textbf{Output}: A compact representation of $\tau(b)$.
\pause
We focus on 2 kinds of constraints of \textcolor{Plum}{$x_{K_i}\in P_{K_i}$}.
\begin{enumerate}
\item Cardinality. \textcolor{Plum}{$x_{K_i}\in P_{K_i}$}→ $\sum_{e\in K_i}x_e\leq p$.
\item Matroid. \textcolor{Plum}{$x_{K_i}\in P_{K_i}$}→ $x_{K_i}$ is in the base polytope of a matroid $M_i$.
\end{enumerate}
\end{frame}
\begin{frame}{Results}
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.
\begin{itemize}
\item Cardinality constraint.
$k=O(mp^{1/3})$ and $\tau$ can be computed in $O((k+m)\log m)$ time.
\item Matroid constraint. $k=O(mr^{1/3})$ and $\tau$ can be computed in $O(Tk+k\log m)$ time.
\end{itemize}
\end{theorem}
\end{frame}
\begin{frame}[plain]
poster
\end{frame}
\end{document}