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An Improved Algorithm for Finding the Closest Pair of Points

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Abstract

As early as in 1975, Shamos and Hoey first gave an O(n lg n)-time divide-and-conquer algorithm (SH algorithm in short) for the problem of finding the closest pair of points. In one process of combination, the Euclidean distances between 3n pairs of points need to be computed, so the overall complexity of computing distance is then 3n lg n. Since the computation of distance is more costly compared with other basic operation, how to improve SH algorithm from the aspect of complexity of computing distance is considered. In 1998, Zhou, Xiong and Zhu improved SH algorithm by reducing this complexity to 2n lg n. In this paper, we make further improvement. The overall complexity of computing distances is reduced to (3n lg n)/2, which is only half that of SH algorithm.

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References

  1. Shamos M I, Hoey D. Closest-point problems. In Proc. 16th IEEE Annu. Symp. Found. Comput. Sci., Berkeley, US, 1975, pp.151–162.

  2. Franco P Preparata, Michael Ian Shamos. Computational Geometry: An Introduction, Springer-Verlag, 1985.

  3. Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, Clifford Stein. Introduction to Algorithms, Second Edition, MIT Press, 2001.

  4. Alsuwaiyel M H. Algorithms Design Techniques and Analysis. World Scientific Publishing Press, 1999.

  5. Yulin Zhou, Pengrong Xiong, Hong Zhu. An improved algorithm about the closest pair of points on plane set. Computer Research and Development, 1998, 35(10): 957–960. (in Chinese)

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Fudan University, Shanghai, 200433, P.R. China

    Qi Ge, Hai-Tao Wang & Hong Zhu

Authors
  1. Qi Ge
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  2. Hai-Tao Wang
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  3. Hong Zhu
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Corresponding author

Correspondence to Qi Ge.

Additional information

This work is supported by the National Natural Science Foundation of China (Grant No. 60496321) and Shanghai Science and Technology Development Fund (Grant No. 025115032).

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Ge, Q., Wang, HT. & Zhu, H. An Improved Algorithm for Finding the Closest Pair of Points. J Comput Sci Technol 21, 27–31 (2006). https://doi.org/10.1007/s11390-006-0027-7

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  • DOI: https://doi.org/10.1007/s11390-006-0027-7

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