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Sequential and parallel algorithms for the k closest pairs problem

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44909

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

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45509

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

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MPI-I-92-134.pdf
(Any fulltext), 12MB

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Citation

Lenhof, H.-P., & Smid, M.(1992). Sequential and parallel algorithms for the k closest pairs problem (MPI-I-92-134). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B708-9
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 $n \choose 2$. A new and simpler proof is given of Salowe's theorem, i.e., a sequential 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. Salowe's algorithm seems difficult to parallelize. A parallel version of our algorithm is given for the CRCW-PRAM model. This version runs in $O((\log n)^{2} \log\log n )$ expected parallel time and has an $O(n \log n \log\log n +k)$ time-processor product.