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Enumerating the k closest pairs mechanically

Smid, Michiel and Lenhof, Hans-Peter

May 1992, 12 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 $n \choose 2$. An 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.

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  AUTHOR = {Smid, Michiel and Lenhof, Hans-Peter},
  TITLE = {Enumerating the k closest pairs mechanically},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-92-118},
  MONTH = {May},
  YEAR = {1992},
  ISSN = {0946-011X},