MPI-I-92-134
Sequential and parallel algorithms for the k closest pairs problem
Lenhof, Hans-Peter and Smid, Michiel
August 1992, 18 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 $n \choose 2$.
A new and simpler proof is given of Salowe's theorem, i.e.,
a sequential 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. Salowe's algorithm seems difficult to
parallelize. A parallel version of our
algorithm is given for the CRCW-PRAM model. This version
runs in $O((\log n)^{2} \log\log n )$
expected parallel time and has an $O(n \log n \log\log n +k)$
time-processor product.
URL to this document: https://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1992-134
BibTeX
@TECHREPORT{LenhofSmid92b,
AUTHOR = {Lenhof, Hans-Peter and Smid, Michiel},
TITLE = {Sequential and parallel algorithms for the k closest pairs problem},
TYPE = {Research Report},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},
NUMBER = {MPI-I-92-134},
MONTH = {August},
YEAR = {1992},
ISSN = {0946-011X},
}