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										79
									
								
								poster.tex
									
									
									
									
									
								
							
							
						
						
									
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								poster.tex
									
									
									
									
									
								
							@@ -23,7 +23,7 @@
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%==Title, date and authors of the poster=======================================
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					%==Title, date and authors of the poster=======================================
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\title
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					\title
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[IJCAI25, 29 - 31 August 2025, Guangzhou, China] % Conference
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					[34th International Joint Conference on Artificial Intelligence (IJCAI25), 29 - 31 August 2025, Guangzhou, China] % Conference
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{ % Poster title
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					{ % Poster title
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Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints
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					Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints
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}
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					}
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@@ -36,6 +36,10 @@ Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinalit
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\begin{document}
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					\begin{document}
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					% larger font
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					\Large
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\begin{frame}[t]
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					\begin{frame}[t]
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%==============================================================================
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					%==============================================================================
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\begin{multicols}{2}
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					\begin{multicols}{2}
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@@ -45,78 +49,7 @@ Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinalit
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\section{Introduction}
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					\section{Introduction}
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\lipsum
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					\lipsum[1-7]
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\begin{equation}
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H = \sum_{i=1}^{N} h_{D}(i) + \sum_{j>i=1}^{N} C_{ij}
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\end{equation}
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In Ref.~\cite{ref1}...
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In Refs.~\cite{ref1,ref2}...
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On webpage~\cite{web}...
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\section{Result and discussions}
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\vskip1ex
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\begin{table}
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\centering
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\caption{This is a table with scientific results.}
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\begin{tabular}{ccccc}
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\hline\hline
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1 & 2 & 3 & 4 & 5\\
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\hline
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aaa & bbb & ccc & ddd & eee\\
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aaaa & bbbb & cccc & dddd & eeee\\
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aaaaa & bbbbb & ccccc & ddddd & eeeee\\
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aaaaaa & bbbbbb & cccccc & dddddd & eeeeee\\
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1.000 & 2.000 & 3.000 & 4.000 & 5.000\\
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\hline\hline
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\end{tabular}
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\end{table}
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\vskip2ex
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blabla
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\vskip1ex
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\begin{figure}
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\centering
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\includegraphics[width=0.99\columnwidth]{./image/landscape.png}
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\caption{This is a picture with scientific results.}
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\end{figure}
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\vskip2ex
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sdfsdf
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\subsection{SubSection, a very very very very very very long title}
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sdfsdf
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\section{Summary and conclusions}
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\lipsum[1-3]
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%==============================================================================
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%==End of content==============================================================
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%==============================================================================
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%--References------------------------------------------------------------------
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\subsection{References}
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\begin{thebibliography}{99}
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\bibitem{ref1} J.~Doe, Article name, \textit{Phys. Rev. Lett.}
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\bibitem{ref2} J.~Doe, J. Smith, Other article name, \textit{Phys. Rev. Lett.}
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\bibitem{web} \url{http://www.google.pl}
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\end{thebibliography}
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%--End of references-----------------------------------------------------------
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\end{multicols}
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					\end{multicols}
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										74
									
								
								slides.tex
									
									
									
									
									
								
							
							
						
						
									
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								slides.tex
									
									
									
									
									
								
							@@ -3,9 +3,10 @@
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\usetheme{Slides}
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					\usetheme{Slides}
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\usepackage{algo}
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					\usepackage{algo}
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\usepackage{soul}
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					\usepackage{soul}
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					% \usepackage{cancel}
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\title[Incentive allocation]{Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints}
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					\title[Incentive allocation]{Large-Scale Trade-Off Curve Computation for Incentive Allocation with Cardinality and Matroid Constraints}
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\date{\today}
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					\date{August 30, 2025}
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\author{\underline{Yu Cong}, Chao Xu, Yi Zhou}
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					\author{\underline{Yu Cong}, Chao Xu, Yi Zhou}
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\institute[UESTC]{University of Electronic Science and Technology of China}
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					\institute[UESTC]{University of Electronic Science and Technology of China}
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% \AtBeginSection[]{
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					% \AtBeginSection[]{
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\begin{document}
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					\begin{document}
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\begin{frame}[plain]
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					\begin{frame}[plain]
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    \titlepage
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					    \titlepage
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					    \scriptsize 34th International Joint Conference on Artificial Intelligence (IJCAI25)
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\end{frame}
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					\end{frame}
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\begin{frame}{title ggg fff}
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					% introduce the problem. 3 things: trade-off curve, approximation, general constraints
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    \ul{sdfggg}
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					\begin{frame}{Incentive allocation with constraints}
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					A ride sharing company wants to send riders promotional coupons in the hope of more rides.
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					%  each agent gets at most 1 coupon.
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					\begin{figure}
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					placeholder\\
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					\includegraphics[width=.5\textwidth]{image/landscape.png}
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					\end{figure}
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					\end{frame}
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					\begin{frame}{Multiple-choice knapsack}
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					\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 $b\in \Z_+$.
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					\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 $\sum_{e\in K} c_e\leq b$.
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					\vspace{1em}
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					\pause
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					Three problems with this modeling:
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					\begin{enumerate}
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					\item Finding the exact optimum is NP-hard. So we consider solving it approximately.
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					\item Companies may run multiple campaigns at the same time. So a trade-off curve between budget and profit will be useful.
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					\item The multiple-choice constraint \textcolor{Red}{$|K\cap K_i|\leq 1$} is too weak for real applications.
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					\end{enumerate}
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					\end{frame}
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					\begin{frame}{Linear programming formulation}
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					\textcolor{gray}{
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					\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 $b\in \Z_+$.}
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					}
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					\pause
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					\begin{equation*}
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					\begin{aligned}
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					\tau(b)= \max_x&    &   v\cdot x&   &   &\\
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					s.t.&   &   c\cdot x&\leq b     &   &\\
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					&   &       \textcolor{Plum}{x_{K_i}}&\textcolor{Plum}{\in P_{K_i}} &   &\forall i\in [n]\\
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					\end{aligned}
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					\end{equation*}
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					\textbf{Output}: A compact representation of $\tau(b)$.
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					\pause
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					We focus on 2 kinds of constraints of \textcolor{Plum}{$x_{K_i}\in P_{K_i}$}.
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					\begin{enumerate}
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					\item Cardinality. \textcolor{Plum}{$x_{K_i}\in P_{K_i}$}→ $\sum_{e\in K_i}x_e\leq p$.
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					\item Matroid. \textcolor{Plum}{$x_{K_i}\in P_{K_i}$}→ $x_{K_i}$ is in the base polytope of a matroid $M_i$.
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					\end{enumerate} 
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					\end{frame}
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					\begin{frame}{Results}
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					We compute the curve $\tau(b)$ fast.
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					\begin{theorem}
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					Consider an incentive allocation problem with a total of $m$ incentives. 
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					The trade-off curve is piecewise linear concave function with $k$ breakpoints.
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					\begin{itemize}
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					\item Cardinality constraint.
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					$k=O(mp^{1/3})$ and $\tau$ can be computed in $O((k+m)\log m)$ time.
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					\item Matroid constraint. $k=O(mr^{1/3})$ and $\tau$ can be computed in $O(Tk+k\log m)$ time.
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					\end{itemize} 
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					\end{theorem}
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					\end{frame}
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					\begin{frame}[plain]
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					poster
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\end{frame}
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					\end{frame}
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\end{document}
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					\end{document}
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