Abstract:
We study the fundamental problem of sorting in a sequential model of computation and in particular consider the time-space trade-off (product of time and space) for this problem.
Beame has shown a lower
bound of 
for this product leaving a gap of a logarithmic factor
up to the previously best known upper bound of 
due to
Frederickson. Since then, no progress has been made towards tightening this
gap.
The main contribution of this paper is a comparison based sorting
algorithm which closes this gap by meeting the lower bound of Beame. The
time-space product 
upper bound holds for the full range of space
bounds between 
and 
. Hence in this range our algorithm is
optimal for comparison based models as well as for the very powerful general
models considered by Beame
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