From 9bf59bc7b44b84fadbcc642579bb54ee1d998825 Mon Sep 17 00:00:00 2001
From: Yu Cong <sxlxcsxlxc@gmail.com>
Date: Thu, 14 Aug 2025 12:43:07 +0800
Subject: [PATCH] ex1.2

---
 main.tex | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/main.tex b/main.tex
index 456147f..4471013 100644
--- a/main.tex
+++ b/main.tex
@@ -37,7 +37,12 @@ The last line is greater than $(\sqrt{d}/5)^d$ for large enough $d$.
 \end{proof}
 
 \begin{exercise}
-Compute clustering radius
+Compute clustering radius.
+Let $C$ and $P$ be two given set of points such that $k=|C|$ and $n=|P|$. Define the covering radius of $P$ by $C$ as $r=\max_{p\in P} \min_{c\in C} \norm{p-c}$.
+\begin{enumerate}
+\item find an $O(n+k\log n)$ expected time alg that outputs $\alpha$ such that $\alpha \leq r \leq 10\alpha$.
+\item for prescribed $\varepsilon>0$, find an $O(n+k\varepsilon^{-2}\log n)$ expected time alg that outputs $\alpha$ s.t. $\alpha<r<(1+\epsilon)\alpha$.
+\end{enumerate}
 \end{exercise}