MPI-INF/SWS Research Reports 1991-2021

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Finding k points with a smallest enclosing square

Smid, Michiel

November 1992, 8 pages.

Status: available - back from printing

An algorithm is presented that, given a set of $n$ points in the plane and an integer $k$, $2 \leq k \leq n$, finds $k$ points with a smallest enclosing axes-parallel square. The algorithm has a running time of $O(n \log n + kn \log^{2} k)$ and uses $O(n)$ space. The previously best known algorithm for this problem takes $O(k^{2} n \log n)$ time and uses $O(kn)$ space.

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  AUTHOR = {Smid, Michiel},
  TITLE = {Finding k points with a smallest enclosing square},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-92-152},
  MONTH = {November},
  YEAR = {1992},
  ISSN = {0946-011X},