MPII93116
Finding k points with a smallest enclosing square
Smid, Michiel
March 1993, 17 pages.
.
Status: available  back from printing
Let $S$ be a set of $n$ points in $d$space, let $R$ be an
axesparallel hyperrectangle 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 doublyexponential 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.

MPII93116.pdf
 Attachement: MPII93116.dvi.gz (13 KBytes); MPII93116.pdf (72 KBytes)
URL to this document: https://domino.mpiinf.mpg.de/internet/reports.nsf/NumberView/1993116
BibTeX
@TECHREPORT{Smid93
,
AUTHOR = {Smid, Michiel},
TITLE = {Finding k points with a smallest enclosing square},
TYPE = {Research Report},
INSTITUTION = {MaxPlanckInstitut f{\"u}r Informatik},
ADDRESS = {Im Stadtwald, D66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPII93116},
MONTH = {March},
YEAR = {1993},
ISSN = {0946011X},
}