Sequential and parallel algorithms for the k closest pairs problem

@article{Lenhof1995SequentialAP,
  title={Sequential and parallel algorithms for the k closest pairs problem},
  author={Hans-Peter Lenhof and Michiel H. M. Smid},
  journal={Int. J. Comput. Geometry Appl.},
  year={1995},
  volume={5},
  pages={273-288}
}
Let S be a set of n points in D-dimensional space, where D is a constant, and let k be an integer between 1 and (~). A new and simpler proof is given of Salowe's theorem, i.e., a sequential algorithmis given that computes the k c10sest pairs in the set S in O(nlogn + k) time, using O(n + k) space. The algorithm fits in the algebraic decision tree model and is, therefore, optimal. Salowe's algorithm seems difficult to parallelize. A parallel version of our algorithm is given for the CRCW-PRAM… CONTINUE READING

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