BIB-VERSION:: CS-TR-v2.0
ID:: ncstrl.dartmouthcs//TR2003-444
ENTRY:: April 11, 2003
ORGANIZATION:: Dartmouth College, Computer Science
TITLE:: Stupid Columnsort Tricks
TYPE:: Technical Report (paper)
REVISION:: 1
AUTHOR:: Chaudhry, Geeta
AUTHOR:: Cormen, Thomas H. 
DATE:: April 2003
RETRIEVAL:: For a paper copy, email <reports@cs.dartmouth.edu>
RETRIEVAL:: For a paper copy, write to
       Technical Report Librarian
       Department of Computer Science
       Dartmouth College
       6211 Sudikoff Laboratory
       Hanover, NH 03755-3510
       USA
RETRIEVAL:: Compressed Postscript at http://www.cs.dartmouth.edu/reports/TR2003-444.ps.Z
RETRIEVAL:: PDF at http://www.cs.dartmouth.edu/reports/TR2003-444.pdf
ABSTRACT:: 
Leighton's columnsort algorithm sorts on an $r \times s$ mesh, subject
to the restrictions that $s$ is a divisor of~$r$ and that $r \geq
2s^2$ (so that the mesh is tall and thin).  We show how to mitigate
both of these restrictions.  One result is that the requirement that
$s$ is a divisor of~$r$ is unnecessary; columnsort sorts correctly
whether or not $s$ divides~$r$.  We present two algorithms that, as
long as $s$ is a perfect square, relax the restriction that $r \geq
2s^2$; both reduce the exponent of~$s$ to~$3/2$.  One algorithm
requires $r \geq 4s^{3/2}$ if $s$ divides~$r$ and $r \geq 6s^{3/2}$ if
$s$ does not divide~$r$.  The other algorithm requires $r \geq
4^{3/2}$, and it requires $s$ to be a divisor of~$r$.  Both algorithms
have applications in increasing the maximum problem size in
out-of-core sorting programs.
END:: ncstrl.dartmouthcs//TR2003-444