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Journal of Computer Science and Technology

, Volume 21, Issue 1, pp 27–31 | Cite as

An Improved Algorithm for Finding the Closest Pair of Points

  • Qi GeEmail author
  • Hai-Tao Wang
  • Hong Zhu
Article

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.

Keywords

Shamos and Hoey algorithm divide and conquer closest pair of points complexity 

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References

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    Shamos M I, Hoey D. Closest-point problems. In Proc. 16th IEEE Annu. Symp. Found. Comput. Sci., Berkeley, US, 1975, pp.151–162.Google Scholar
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    Franco P Preparata, Michael Ian Shamos. Computational Geometry: An Introduction, Springer-Verlag, 1985.Google Scholar
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    Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, Clifford Stein. Introduction to Algorithms, Second Edition, MIT Press, 2001.Google Scholar
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    Alsuwaiyel M H. Algorithms Design Techniques and Analysis. World Scientific Publishing Press, 1999.Google Scholar
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    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)Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringFudan UniversityShanghaiP.R. China

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