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\title{Closest Pair of Points Algorithms}
\author{Martin Rau and Tobias Nipkow}
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\begin{abstract}
This entry provides two related verified divide-and-conquer algorithms solving
the fundamental \textit{Closest Pair of Points} problem in Computational Geometry.
Functional correctness and the optimal running time of $\mathcal{O}(n \log n)$ are proved. 
Executable code is generated which is empirically competitive with handwritten
reference implementations.
\end{abstract}

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