MPI-INF/SWS Research Reports 1991-2021

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Sequential and parallel algorithms for the k closest pairs problem

Lenhof, Hans-Peter and Smid, Michiel

August 1992, 18 pages.

Status: available - back from printing

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 $n \choose 2$. A new and simpler proof is given of Salowe's theorem, i.e., a sequential algorithm is given that computes the $k$ closest pairs in the set $S$ in $O(n \log n + k)$ 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 model. This version runs in $O((\log n)^{2} \log\log n )$ expected parallel time and has an $O(n \log n \log\log n +k)$ time-processor product.

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  AUTHOR = {Lenhof, Hans-Peter and Smid, Michiel},
  TITLE = {Sequential and parallel algorithms for the k closest pairs problem},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-92-134},
  MONTH = {August},
  YEAR = {1992},
  ISSN = {0946-011X},