Enumerating the k closest pairs mechanically

Smid, Michiel; Lenhof, Hans-Peter

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Enumerating the k closest pairs mechanically

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Smid, Michiel
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Lenhof, Hans-Peter
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Smid, M., & Lenhof, H.-P.(1992). Enumerating the k closest pairs mechanically (MPI-I-92-118). Saarbrücken: Max-Planck-Institut für Informatik.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-B6F1-3

Abstract

Let $S$ be a set of $n$ points in $D$-dimensional space, where $D$ is a constant, and let $k$ be an integer between $1$ and $n \choose 2$. An algorithm is given that computes the $k$ closest pairs in the set $S$ in $O(n \log n + k)$ time, using $O(n+k)$ space. The algorithm fits in the algebraic decision tree model and is, therefore, optimal.