Simple randomized algorithms for closest pair problems

Golin, Mordecai J.; Raman, Rajeev; Schwarz, Christian; Smid, Michiel

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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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フルテキスト (公開)

MPI-92-155.pdf
(全文テキスト（全般）), 19MB

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引用

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.

引用: https://hdl.handle.net/11858/00-001M-0000-0014-B723-B

要旨

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.