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\begin{center} \Large
{\scshape 6.851 Advanced Data Structures (Spring'12)} \\[1ex]
{Prof.~Erik Demaine \qquad TAs: Tom Morgan, Justin Zhang} \\[2ex]
\framebox{Problem 2} \quad {\em Due: Thursday, Mar.\ 1}
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Be sure to read the instructions on the assignments section of the
class web page.

\paragraph{Range tree construction.}

Recall that in class we presented the range tree and the layered range tree for answering orthogonal range trees.  However, we did not describe how to construct them efficiently.

\begin{enumerate}
\item Describe how to construct a $d$-dimensional range tree on $n$ given points
 in $O(n \lg^{d-1} n)$ time.
\item Describe how to construct a $d$-dimensional layered range tree on
 $n$ given points in $O(n \lg^{d-1} n)$ time.
\end{enumerate}

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