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Finding k points with a smallest enclosing square

Smid, Michiel

MPI-I-93-116. March 1993, 17 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
Let $S$ be a set of $n$ points in $d$-space, let $R$ be an
axes-parallel hyper-rectangle and let $1 \leq k \leq n$ be an
integer. An algorithm is given that decides if $R$ can be
translated such that it contains at least $k$ points of $S$.
After a presorting step, this algorithm runs in $O(n)$ time,
with a constant factor that is doubly-exponential in~$d$.
Two applications are given. First, a translate of $R$
containing the maximal number of points can be computed
in $O(n \log n)$ time. Second, a $k$-point subset of $S$
with minimal $L_{\infty}$-diameter can be computed, also
in $O(n \log n)$ time. Using known dynamization techniques,
the latter result gives improved dynamic data structures
for maintaining such a $k$-point subset.
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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-93-116},
  MONTH = {March},
  YEAR = {1993},
  ISSN = {0946-011X},