From 0ddd9301195ae15c845ce10f7c8983e3fcad200a Mon Sep 17 00:00:00 2001
From: Yu Cong <sxlxcsxlxc@gmail.com>
Date: Fri, 22 Aug 2025 10:29:54 +0800
Subject: [PATCH] update action & fix typo

---
 .gitea/workflows/compile.yml | 2 +-
 poster.tex                   | 6 +++---
 slides.tex                   | 2 +-
 3 files changed, 5 insertions(+), 5 deletions(-)

diff --git a/.gitea/workflows/compile.yml b/.gitea/workflows/compile.yml
index ccdcb29..2af8e51 100644
--- a/.gitea/workflows/compile.yml
+++ b/.gitea/workflows/compile.yml
@@ -7,7 +7,7 @@ jobs:
 
     steps:
       - name: Check out the repository
-        uses: actions/checkout@v4
+        uses: sxlxc/checkout@v4
 
       - name: Compile LaTeX using local TeX Live
         # These commands run directly in your machine's shell
diff --git a/poster.tex b/poster.tex
index 4045367..c7ad6bc 100644
--- a/poster.tex
+++ b/poster.tex
@@ -49,10 +49,10 @@
 \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.
@@ -101,7 +101,7 @@ 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.
 
diff --git a/slides.tex b/slides.tex
index d7d1310..584fd73 100644
--- a/slides.tex
+++ b/slides.tex
@@ -47,7 +47,7 @@ A ride sharing company wants to send riders promotional coupons in the hope of m
 \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 $\sum_{e\in K} c_e$ while satisfying \textcolor{Red}{$|K\cap K_i|\leq 1$} and $\sum_{e\in K} c_e\leq b$.
 
 \vspace{1em}
 \pause