# MPI-I-93-116

## 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.

Acknowledgement:** **

References to related material:

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1993-116

**BibTeX**
`@TECHREPORT{``Smid93`

`,`

` 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},`

`}`