sxlxc/ijcai25-slides-poster
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update action & fix typo
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Yu Cong
2025-08-22 10:29:54 +08:00
parent 1361b5fac1
commit 0ddd930119
3 changed files with 5 additions and 5 deletions
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2
.gitea/workflows/compile.yml
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@@ -7,7 +7,7 @@ jobs:
steps: steps:
- name: Check out the repository - name: Check out the repository
uses: actions/checkout@v4 uses: sxlxc/checkout@v4
- name: Compile LaTeX using local TeX Live - name: Compile LaTeX using local TeX Live
# These commands run directly in your machine's shell # These commands run directly in your machine's shell

6
poster.tex
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@@ -49,10 +49,10 @@
\section{Problem} \section{Problem}
We consider the incentive allocation problem with additional constraints. 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}{ \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. This problem is NP-hard. Consider its LP relaxation.
@@ -101,7 +101,7 @@ We consider 3 cases of additional constraints $x_{E_i}\in \mathcal{F}_i$ :
\end{table} \end{table}
\section{Methods} \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{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.

2
slides.tex
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@@ -47,7 +47,7 @@ A ride sharing company wants to send riders promotional coupons in the hope of m
\begin{frame}{Multiple-choice knapsack} \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{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 $\sum_{e\in K} c_e$ while satisfying \textcolor{Red}{$|K\cap K_i|\leq 1$} and $\sum_{e\in K} c_e\leq b$.
\vspace{1em} \vspace{1em}
\pause \pause