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Yu Cong
2025-09-04 20:15:12 +08:00
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@@ -60,7 +60,6 @@ parameter $k$, present a (simple) randomized algorithm that computes, in expecte
time, a circle $D$ that contains $k$ points of $P$ and $\mathrm{radius}(D) ≤2r_{\mathrm{opt}}(P,k)$. time, a circle $D$ that contains $k$ points of $P$ and $\mathrm{radius}(D) ≤2r_{\mathrm{opt}}(P,k)$.
\end{exercise} \end{exercise}
\section*{Not in the book} \section*{Not in the book}
\begin{problem}[$d$-dimensional rectangle stabbing \cite{gaur_constant_2002}] \begin{problem}[$d$-dimensional rectangle stabbing \cite{gaur_constant_2002}]
Given a set $R$ of $n$ axis-parallel rectangles and a set $\mathcal H$ of axis-parallel $d$ dimensional hyperplanes, find the minimum subset of $\mathcal H$ such that every rectangle is stabbed by at least one hyperplane in the subset. Given a set $R$ of $n$ axis-parallel rectangles and a set $\mathcal H$ of axis-parallel $d$ dimensional hyperplanes, find the minimum subset of $\mathcal H$ such that every rectangle is stabbed by at least one hyperplane in the subset.