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Simple randomized algorithms for closest pair problems

MPS-Authors
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Golin,  Mordecai J.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Raman,  Rajeev
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Schwarz,  Christian
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

/persons/resource/persons45509

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

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MPI-92-155.pdf
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Citation

Golin, M. J., Raman, R., Schwarz, C., & Smid, M.(1992). Simple randomized algorithms for closest pair problems (MPI-I-92-155). Saarbrücken: Max-Planck-Institut für Informatik.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0014-B723-B
Abstract
We present a conceptually simple, randomized incremental algorithm for finding the closest pair in a set of $n$ points in $D$-dimensional space, where $D \geq 2$ is a fixed constant. Using dynamic perfect hashing, the algorithm runs in $O(n)$ expected time. In addition to being quick on the average, this algorithm is reliable: we show that it runs in $O(n \log n / \log\log n)$ time with high probability.