ex1.2

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}