An optimal algorithm for the on-line closest-pair problem

Schwarz, Christian; Smid, Michiel

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An optimal algorithm for the on-line closest-pair problem

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

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

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MPI-I-91-123.pdf
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引用

Schwarz, C., & Smid, M.(1991). An optimal algorithm for the on-line closest-pair problem (MPI-I-91-123). Saarbrücken: Max-Planck-Institut für Informatik.

引用: https://hdl.handle.net/11858/00-001M-0000-0014-B6DA-A

要旨

We give an algorithm that computes the closest pair in a set of $n$ points in $k$-dimensional space on-line, in $O(n \log n)$ ime. The algorithm only uses algebraic functions and, therefore, is optimal. The algorithm maintains a hierarchical subdivision of $k$-space into hyperrectangles, which is stored in a binary tree. Centroids are used to maintain a balanced decomposition of this tree.