@TechReport{Dartmouth:TR2003-445,
  author = {Geeta Chaudhry and Elizabeth A. Hamon and Thomas H. Cormen},
  title = {{Relaxing the Problem-Size Bound for Out-of-Core Columnsort}},
  institution = {Dartmouth College, Computer Science},
  address = {Hanover, NH},
  number = {TR2003-445},
  year = {2003},
  month = {April},
  URL = {http://www.cs.dartmouth.edu/reports/TR2003-445.ps.Z},
  abstract = {
    Previous implementations of out-of-core columnsort limit the problem
    size to $N \leq \sqrt{(M/P)^3 / 2}$, where $N$ is the number of
    records to sort, $P$ is the number of processors, and $M$ is the total
    number of records that the entire system can hold in its memory (so
    that $M/P$ is the number of records that a single processor can hold
    in its memory).  We implemented two variations to out-of-core
    columnsort that relax this restriction.  Subblock columnsort is based
    on an algorithmic modification of the underlying columnsort algorithm,
    and it improves the problem-size bound to $N \leq (M/P)^{5/3} /
    4^{2/3}$ but at the cost of additional disk I/O\@.  $M$-columnsort
    changes the notion of the column size in columnsort, improving the
    maximum problem size to $N \leq \sqrt{M^3 / 2}$ but at the cost of
    additional computation and communication.  Experimental results on a
    Beowulf cluster show that both subblock columnsort and $M$-columnsort
    run well but that $M$-columnsort is faster.  A further advantage of
    $M$-columnsort is that it handles a wider range of problem sizes than
    subblock columnsort.
  }
}